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\\vec{b}}",[574,1879,1881,1900],{"className":1880,"ariaHidden":595},[612],[574,1882,1884,1888,1891,1894,1897],{"className":1883},[616],[574,1885],{"className":1886,"style":1887},[620],"height:0.6944em;",[574,1889,1836],{"className":1890},[625,650],[574,1892],{"className":1893,"style":1149},[1148],[574,1895,978],{"className":1896},[1153],[574,1898],{"className":1899,"style":1149},[1148],[574,1901,1903,1907],{"className":1902},[616],[574,1904],{"className":1905,"style":1906},[620],"height:1.5724em;vertical-align:-0.4942em;",[574,1908,1910,1914,2120],{"className":1909},[625],[574,1911],{"className":1912},[1402,1913],"nulldelimiter",[574,1915,1917],{"className":1916},[1840],[574,1918,1920,2111],{"className":1919},[630,1171],[574,1921,1923,2108],{"className":1922},[634],[574,1924,1927,2012,2023],{"className":1925,"style":1926},[638],"height:1.0782em;",[574,1928,1930,1933],{"style":1929},"top:-2.5058em;",[574,1931],{"className":1932,"style":646},[645],[574,1934,1936],{"className":1935},[1188,1189,1190,1191],[574,1937,1939,1974,1977],{"className":1938},[625,1191],[574,1940,1942],{"className":1941},[625,626,1191],[574,1943,1945],{"className":1944},[630],[574,1946,1948],{"className":1947},[634],[574,1949,1951,1959],{"className":1950,"style":711},[638],[574,1952,1953,1956],{"style":1216},[574,1954],{"className":1955,"style":1220},[645],[574,1957,696],{"className":1958},[625,650,1191],[574,1960,1961,1964],{"style":1226},[574,1962],{"className":1963,"style":1220},[645],[574,1965,1967],{"className":1966,"style":660},[659],[574,1968,1970],{"className":1969,"style":665},[664,1191],[667,1971,1972],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,1973],{"d":678},[574,1975,1852],{"className":1976},[1473,1191],[574,1978,1980],{"className":1979},[625,626,1191],[574,1981,1983],{"className":1982},[630],[574,1984,1986],{"className":1985},[634],[574,1987,1989,1997],{"className":1988,"style":711},[638],[574,1990,1991,1994],{"style":1216},[574,1992],{"className":1993,"style":1220},[645],[574,1995,696],{"className":1996},[625,650,1191],[574,1998,1999,2002],{"style":1226},[574,2000],{"className":2001,"style":1220},[645],[574,2003,2005],{"className":2004,"style":660},[659],[574,2006,2008],{"className":2007,"style":665},[664,1191],[667,2009,2010],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,2011],{"d":678},[574,2013,2015,2018],{"style":2014},"top:-3.23em;",[574,2016],{"className":2017,"style":646},[645],[574,2019],{"className":2020,"style":2022},[2021],"frac-line","border-bottom-width:0.04em;",[574,2024,2026,2029],{"style":2025},"top:-3.394em;",[574,2027],{"className":2028,"style":646},[645],[574,2030,2032],{"className":2031},[1188,1189,1190,1191],[574,2033,2035,2070,2073],{"className":2034},[625,1191],[574,2036,2038],{"className":2037},[625,626,1191],[574,2039,2041],{"className":2040},[630],[574,2042,2044],{"className":2043},[634],[574,2045,2047,2055],{"className":2046,"style":621},[638],[574,2048,2049,2052],{"style":1216},[574,2050],{"className":2051,"style":1220},[645],[574,2053,599],{"className":2054},[625,650,1191],[574,2056,2057,2060],{"style":1216},[574,2058],{"className":2059,"style":1220},[645],[574,2061,2063],{"className":2062,"style":660},[659],[574,2064,2066],{"className":2065,"style":665},[664,1191],[667,2067,2068],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,2069],{"d":678},[574,2071,1852],{"className":2072},[1473,1191],[574,2074,2076],{"className":2075},[625,626,1191],[574,2077,2079],{"className":2078},[630],[574,2080,2082],{"className":2081},[634],[574,2083,2085,2093],{"className":2084,"style":711},[638],[574,2086,2087,2090],{"style":1216},[574,2088],{"className":2089,"style":1220},[645],[574,2091,696],{"className":2092},[625,650,1191],[574,2094,2095,2098],{"style":1226},[574,2096],{"className":2097,"style":1220},[645],[574,2099,2101],{"className":2100,"style":660},[659],[574,2102,2104],{"className":2103,"style":665},[664,1191],[667,2105,2106],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,2107],{"d":678},[574,2109,1389],{"className":2110},[1388],[574,2112,2114],{"className":2113},[634],[574,2115,2118],{"className":2116,"style":2117},[638],"height:0.4942em;",[574,2119],{},[574,2121],{"className":2122},[1441,1913]," ergibt sich aus der Forderung ",[574,2125,2127,2173],{"className":2126},[577],[574,2128,2130],{"className":2129},[581],[583,2131,2132],{"xmlns":585},[587,2133,2134,2170],{},[590,2135,2136,2138,2144,2146,2148,2154,2156,2158,2164,2166],{},[601,2137,1006],{"stretchy":1005},[593,2139,2140,2142],{"accent":595},[597,2141,599],{},[601,2143,603],{},[601,2145,1053],{},[597,2147,1836],{},[593,2149,2150,2152],{"accent":595},[597,2151,696],{},[601,2153,603],{},[601,2155,1015],{"stretchy":1005},[601,2157,1852],{},[593,2159,2160,2162],{"accent":595},[597,2161,696],{},[601,2163,603],{},[601,2165,978],{},[2167,2168,2169],"mn",{},"0",[605,2171,2172],{"encoding":607},"(\\vec{a} - \\lambda \\vec{b}) \\cdot \\vec{b} = 0",[574,2174,2176,2230,2287,2337],{"className":2175,"ariaHidden":595},[612],[574,2177,2179,2183,2186,2221,2224,2227],{"className":2178},[616],[574,2180],{"className":2181,"style":2182},[620],"height:1em;vertical-align:-0.25em;",[574,2184,1006],{"className":2185},[1402],[574,2187,2189],{"className":2188},[625,626],[574,2190,2192],{"className":2191},[630],[574,2193,2195],{"className":2194},[634],[574,2196,2198,2206],{"className":2197,"style":621},[638],[574,2199,2200,2203],{"style":641},[574,2201],{"className":2202,"style":646},[645],[574,2204,599],{"className":2205},[625,650],[574,2207,2208,2211],{"style":641},[574,2209],{"className":2210,"style":646},[645],[574,2212,2214],{"className":2213,"style":660},[659],[574,2215,2217],{"className":2216,"style":665},[664],[667,2218,2219],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,2220],{"d":678},[574,2222],{"className":2223,"style":1469},[1148],[574,2225,1053],{"className":2226},[1473],[574,2228],{"className":2229,"style":1469},[1148],[574,2231,2233,2237,2240,2275,2278,2281,2284],{"className":2232},[616],[574,2234],{"className":2235,"style":2236},[620],"height:1.2274em;vertical-align:-0.25em;",[574,2238,1836],{"className":2239},[625,650],[574,2241,2243],{"className":2242},[625,626],[574,2244,2246],{"className":2245},[630],[574,2247,2249],{"className":2248},[634],[574,2250,2252,2260],{"className":2251,"style":711},[638],[574,2253,2254,2257],{"style":641},[574,2255],{"className":2256,"style":646},[645],[574,2258,696],{"className":2259},[625,650],[574,2261,2262,2265],{"style":734},[574,2263],{"className":2264,"style":646},[645],[574,2266,2268],{"className":2267,"style":660},[659],[574,2269,2271],{"className":2270,"style":665},[664],[667,2272,2273],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,2274],{"d":678},[574,2276,1015],{"className":2277},[1441],[574,2279],{"className":2280,"style":1469},[1148],[574,2282,1852],{"className":2283},[1473],[574,2285],{"className":2286,"style":1469},[1148],[574,2288,2290,2293,2328,2331,2334],{"className":2289},[616],[574,2291],{"className":2292,"style":711},[620],[574,2294,2296],{"className":2295},[625,626],[574,2297,2299],{"className":2298},[630],[574,2300,2302],{"className":2301},[634],[574,2303,2305,2313],{"className":2304,"style":711},[638],[574,2306,2307,2310],{"style":641},[574,2308],{"className":2309,"style":646},[645],[574,2311,696],{"className":2312},[625,650],[574,2314,2315,2318],{"style":734},[574,2316],{"className":2317,"style":646},[645],[574,2319,2321],{"className":2320,"style":660},[659],[574,2322,2324],{"className":2323,"style":665},[664],[667,2325,2326],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,2327],{"d":678},[574,2329],{"className":2330,"style":1149},[1148],[574,2332,978],{"className":2333},[1153],[574,2335],{"className":2336,"style":1149},[1148],[574,2338,2340,2344],{"className":2339},[616],[574,2341],{"className":2342,"style":2343},[620],"height:0.6444em;",[574,2345,2169],{"className":2346},[625],". Ist 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ein Einheitsvektor, vereinfacht sich die Formel zu ",[574,2414,2416,2454],{"className":2415},[577],[574,2417,2419],{"className":2418},[581],[583,2420,2421],{"xmlns":585},[587,2422,2423,2451],{},[590,2424,2425,2427,2433,2435,2441,2443,2445],{},[601,2426,1006],{"stretchy":1005},[593,2428,2429,2431],{"accent":595},[597,2430,599],{},[601,2432,603],{},[601,2434,1852],{},[593,2436,2437,2439],{"accent":595},[597,2438,696],{},[601,2440,603],{},[601,2442,1015],{"stretchy":1005},[1025,2444,1027],{},[593,2446,2447,2449],{"accent":595},[597,2448,696],{},[601,2450,603],{},[605,2452,2453],{"encoding":607},"(\\vec{a} \\cdot \\vec{b})\\, \\vec{b}",[574,2455,2457,2510],{"className":2456,"ariaHidden":595},[612],[574,2458,2460,2463,2466,2501,2504,2507],{"className":2459},[616],[574,2461],{"className":2462,"style":2182},[620],[574,2464,1006],{"className":2465},[1402],[574,2467,2469],{"className":2468},[625,626],[574,2470,2472],{"className":2471},[630],[574,2473,2475],{"className":2474},[634],[574,2476,2478,2486],{"className":2477,"style":621},[638],[574,2479,2480,2483],{"style":641},[574,2481],{"className":2482,"style":646},[645],[574,2484,599],{"className":2485},[625,650],[574,2487,2488,2491],{"style":641},[574,2489],{"className":2490,"style":646},[645],[574,2492,2494],{"className":2493,"style":660},[659],[574,2495,2497],{"className":2496,"style":665},[664],[667,2498,2499],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,2500],{"d":678},[574,2502],{"className":2503,"style":1469},[1148],[574,2505,1852],{"className":2506},[1473],[574,2508],{"className":2509,"style":1469},[1148],[574,2511,2513,2516,2551,2554,2557],{"className":2512},[616],[574,2514],{"className":2515,"style":2236},[620],[574,2517,2519],{"className":2518},[625,626],[574,2520,2522],{"className":2521},[630],[574,2523,2525],{"className":2524},[634],[574,2526,2528,2536],{"className":2527,"style":711},[638],[574,2529,2530,2533],{"style":641},[574,2531],{"className":2532,"style":646},[645],[574,2534,696],{"className":2535},[625,650],[574,2537,2538,2541],{"style":734},[574,2539],{"className":2540,"style":646},[645],[574,2542,2544],{"className":2543,"style":660},[659],[574,2545,2547],{"className":2546,"style":665},[664],[667,2548,2549],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,2550],{"d":678},[574,2552,1015],{"className":2553},[1441],[574,2555],{"className":2556,"style":1815},[1148],[574,2558,2560],{"className":2559},[625,626],[574,2561,2563],{"className":2562},[630],[574,2564,2566],{"className":2565},[634],[574,2567,2569,2577],{"className":2568,"style":711},[638],[574,2570,2571,2574],{"style":641},[574,2572],{"className":2573,"style":646},[645],[574,2575,696],{"className":2576},[625,650],[574,2578,2579,2582],{"style":734},[574,2580],{"className":2581,"style":646},[645],[574,2583,2585],{"className":2584,"style":660},[659],[574,2586,2588],{"className":2587,"style":665},[664],[667,2589,2590],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,2591],{"d":678},[565,2593,2594],{},"Eigenschaften und Anwendungen:",[2596,2597,2598,3149,3381,3772],"ul",{},[2599,2600,2601,2602,2847,2848,3079,3080,3083,3084,3148],"li",{},"Die Länge der Projektion ist ",[574,2603,2605,2652],{"className":2604},[577],[574,2606,2608],{"className":2607},[581],[583,2609,2610],{"xmlns":585},[587,2611,2612,2649],{},[590,2613,2614],{},[1840,2615,2616,2637],{},[590,2617,2618,2621,2627,2629,2635],{},[597,2619,2620],{"mathvariant":993},"∣",[593,2622,2623,2625],{"accent":595},[597,2624,599],{},[601,2626,603],{},[601,2628,1852],{},[593,2630,2631,2633],{"accent":595},[597,2632,696],{},[601,2634,603],{},[597,2636,2620],{"mathvariant":993},[590,2638,2639,2641,2647],{},[597,2640,2620],{"mathvariant":993},[593,2642,2643,2645],{"accent":595},[597,2644,696],{},[601,2646,603],{},[597,2648,2620],{"mathvariant":993},[605,2650,2651],{"encoding":607},"\\frac{|\\vec{a} \\cdot \\vec{b}|}{|\\vec{b}|}",[574,2653,2655],{"className":2654,"ariaHidden":595},[612],[574,2656,2658,2662],{"className":2657},[616],[574,2659],{"className":2660,"style":2661},[620],"height:1.8384em;vertical-align:-0.6692em;",[574,2663,2665,2668,2844],{"className":2664},[625],[574,2666],{"className":2667},[1402,1913],[574,2669,2671],{"className":2670},[1840],[574,2672,2674,2835],{"className":2673},[630,1171],[574,2675,2677,2832],{"className":2676},[634],[574,2678,2681,2733,2741],{"className":2679,"style":2680},[638],"height:1.1692em;",[574,2682,2683,2686],{"style":1929},[574,2684],{"className":2685,"style":646},[645],[574,2687,2689],{"className":2688},[1188,1189,1190,1191],[574,2690,2692,2695,2730],{"className":2691},[625,1191],[574,2693,2620],{"className":2694},[625,1191],[574,2696,2698],{"className":2697},[625,626,1191],[574,2699,2701],{"className":2700},[630],[574,2702,2704],{"className":2703},[634],[574,2705,2707,2715],{"className":2706,"style":711},[638],[574,2708,2709,2712],{"style":1216},[574,2710],{"className":2711,"style":1220},[645],[574,2713,696],{"className":2714},[625,650,1191],[574,2716,2717,2720],{"style":1226},[574,2718],{"className":2719,"style":1220},[645],[574,2721,2723],{"className":2722,"style":660},[659],[574,2724,2726],{"className":2725,"style":665},[664,1191],[667,2727,2728],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,2729],{"d":678},[574,2731,2620],{"className":2732},[625,1191],[574,2734,2735,2738],{"style":2014},[574,2736],{"className":2737,"style":646},[645],[574,2739],{"className":2740,"style":2022},[2021],[574,2742,2744,2747],{"style":2743},"top:-3.485em;",[574,2745],{"className":2746,"style":646},[645],[574,2748,2750],{"className":2749},[1188,1189,1190,1191],[574,2751,2753,2756,2791,2794,2829],{"className":2752},[625,1191],[574,2754,2620],{"className":2755},[625,1191],[574,2757,2759],{"className":2758},[625,626,1191],[574,2760,2762],{"className":2761},[630],[574,2763,2765],{"className":2764},[634],[574,2766,2768,2776],{"className":2767,"style":621},[638],[574,2769,2770,2773],{"style":1216},[574,2771],{"className":2772,"style":1220},[645],[574,2774,599],{"className":2775},[625,650,1191],[574,2777,2778,2781],{"style":1216},[574,2779],{"className":2780,"style":1220},[645],[574,2782,2784],{"className":2783,"style":660},[659],[574,2785,2787],{"className":2786,"style":665},[664,1191],[667,2788,2789],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,2790],{"d":678},[574,2792,1852],{"className":2793},[1473,1191],[574,2795,2797],{"className":2796},[625,626,1191],[574,2798,2800],{"className":2799},[630],[574,2801,2803],{"className":2802},[634],[574,2804,2806,2814],{"className":2805,"style":711},[638],[574,2807,2808,2811],{"style":1216},[574,2809],{"className":2810,"style":1220},[645],[574,2812,696],{"className":2813},[625,650,1191],[574,2815,2816,2819],{"style":1226},[574,2817],{"className":2818,"style":1220},[645],[574,2820,2822],{"className":2821,"style":660},[659],[574,2823,2825],{"className":2824,"style":665},[664,1191],[667,2826,2827],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,2828],{"d":678},[574,2830,2620],{"className":2831},[625,1191],[574,2833,1389],{"className":2834},[1388],[574,2836,2838],{"className":2837},[634],[574,2839,2842],{"className":2840,"style":2841},[638],"height:0.6692em;",[574,2843],{},[574,2845],{"className":2846},[1441,1913],". Ohne Betrag heißt ",[574,2849,2851,2893],{"className":2850},[577],[574,2852,2854],{"className":2853},[581],[583,2855,2856],{"xmlns":585},[587,2857,2858,2890],{},[590,2859,2860],{},[1840,2861,2862,2878],{},[590,2863,2864,2870,2872],{},[593,2865,2866,2868],{"accent":595},[597,2867,599],{},[601,2869,603],{},[601,2871,1852],{},[593,2873,2874,2876],{"accent":595},[597,2875,696],{},[601,2877,603],{},[590,2879,2880,2882,2888],{},[597,2881,2620],{"mathvariant":993},[593,2883,2884,2886],{"accent":595},[597,2885,696],{},[601,2887,603],{},[597,2889,2620],{"mathvariant":993},[605,2891,2892],{"encoding":607},"\\frac{\\vec{a} \\cdot \\vec{b}}{|\\vec{b}|}",[574,2894,2896],{"className":2895,"ariaHidden":595},[612],[574,2897,2899,2903],{"className":2898},[616],[574,2900],{"className":2901,"style":2902},[620],"height:1.7474em;vertical-align:-0.6692em;",[574,2904,2906,2909,3076],{"className":2905},[625],[574,2907],{"className":2908},[1402,1913],[574,2910,2912],{"className":2911},[1840],[574,2913,2915,3068],{"className":2914},[630,1171],[574,2916,2918,3065],{"className":2917},[634],[574,2919,2921,2973,2981],{"className":2920,"style":1926},[638],[574,2922,2923,2926],{"style":1929},[574,2924],{"className":2925,"style":646},[645],[574,2927,2929],{"className":2928},[1188,1189,1190,1191],[574,2930,2932,2935,2970],{"className":2931},[625,1191],[574,2933,2620],{"className":2934},[625,1191],[574,2936,2938],{"className":2937},[625,626,1191],[574,2939,2941],{"className":2940},[630],[574,2942,2944],{"className":2943},[634],[574,2945,2947,2955],{"className":2946,"style":711},[638],[574,2948,2949,2952],{"style":1216},[574,2950],{"className":2951,"style":1220},[645],[574,2953,696],{"className":2954},[625,650,1191],[574,2956,2957,2960],{"style":1226},[574,2958],{"className":2959,"style":1220},[645],[574,2961,2963],{"className":2962,"style":660},[659],[574,2964,2966],{"className":2965,"style":665},[664,1191],[667,2967,2968],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,2969],{"d":678},[574,2971,2620],{"className":2972},[625,1191],[574,2974,2975,2978],{"style":2014},[574,2976],{"className":2977,"style":646},[645],[574,2979],{"className":2980,"style":2022},[2021],[574,2982,2983,2986],{"style":2025},[574,2984],{"className":2985,"style":646},[645],[574,2987,2989],{"className":2988},[1188,1189,1190,1191],[574,2990,2992,3027,3030],{"className":2991},[625,1191],[574,2993,2995],{"className":2994},[625,626,1191],[574,2996,2998],{"className":2997},[630],[574,2999,3001],{"className":3000},[634],[574,3002,3004,3012],{"className":3003,"style":621},[638],[574,3005,3006,3009],{"style":1216},[574,3007],{"className":3008,"style":1220},[645],[574,3010,599],{"className":3011},[625,650,1191],[574,3013,3014,3017],{"style":1216},[574,3015],{"className":3016,"style":1220},[645],[574,3018,3020],{"className":3019,"style":660},[659],[574,3021,3023],{"className":3022,"style":665},[664,1191],[667,3024,3025],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,3026],{"d":678},[574,3028,1852],{"className":3029},[1473,1191],[574,3031,3033],{"className":3032},[625,626,1191],[574,3034,3036],{"className":3035},[630],[574,3037,3039],{"className":3038},[634],[574,3040,3042,3050],{"className":3041,"style":711},[638],[574,3043,3044,3047],{"style":1216},[574,3045],{"className":3046,"style":1220},[645],[574,3048,696],{"className":3049},[625,650,1191],[574,3051,3052,3055],{"style":1226},[574,3053],{"className":3054,"style":1220},[645],[574,3056,3058],{"className":3057,"style":660},[659],[574,3059,3061],{"className":3060,"style":665},[664,1191],[667,3062,3063],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,3064],{"d":678},[574,3066,1389],{"className":3067},[1388],[574,3069,3071],{"className":3070},[634],[574,3072,3074],{"className":3073,"style":2841},[638],[574,3075],{},[574,3077],{"className":3078},[1441,1913]," ",[569,3081,3082],{},"Skalarprojektion","; ihr Vorzeichen zeigt, ob die Projektion in oder gegen die Richtung von ",[574,3085,3087,3104],{"className":3086},[577],[574,3088,3090],{"className":3089},[581],[583,3091,3092],{"xmlns":585},[587,3093,3094,3102],{},[590,3095,3096],{},[593,3097,3098,3100],{"accent":595},[597,3099,696],{},[601,3101,603],{},[605,3103,701],{"encoding":607},[574,3105,3107],{"className":3106,"ariaHidden":595},[612],[574,3108,3110,3113],{"className":3109},[616],[574,3111],{"className":3112,"style":711},[620],[574,3114,3116],{"className":3115},[625,626],[574,3117,3119],{"className":3118},[630],[574,3120,3122],{"className":3121},[634],[574,3123,3125,3133],{"className":3124,"style":711},[638],[574,3126,3127,3130],{"style":641},[574,3128],{"className":3129,"style":646},[645],[574,3131,696],{"className":3132},[625,650],[574,3134,3135,3138],{"style":734},[574,3136],{"className":3137,"style":646},[645],[574,3139,3141],{"className":3140,"style":660},[659],[574,3142,3144],{"className":3143,"style":665},[664],[667,3145,3146],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,3147],{"d":678}," zeigt.",[2599,3150,3151,3152,3380],{},"Die Abbildung ",[574,3153,3155,3200],{"className":3154},[577],[574,3156,3158],{"className":3157},[581],[583,3159,3160],{"xmlns":585},[587,3161,3162,3197],{},[590,3163,3164,3170,3173,3187,3189,3195],{},[593,3165,3166,3168],{"accent":595},[597,3167,599],{},[601,3169,603],{},[601,3171,3172],{},"↦",[987,3174,3175,3181],{},[590,3176,3177,3179],{},[597,3178,555],{"mathvariant":993},[601,3180,996],{},[593,3182,3183,3185],{"accent":595},[597,3184,696],{},[601,3186,603],{},[601,3188,1006],{"stretchy":1005},[593,3190,3191,3193],{"accent":595},[597,3192,599],{},[601,3194,603],{},[601,3196,1015],{"stretchy":1005},[605,3198,3199],{"encoding":607},"\\vec{a} \\mapsto \\operatorname{proj}_{\\vec{b}}(\\vec{a})",[574,3201,3203,3254],{"className":3202,"ariaHidden":595},[612],[574,3204,3206,3210,3245,3248,3251],{"className":3205},[616],[574,3207],{"className":3208,"style":3209},[620],"height:0.725em;vertical-align:-0.011em;",[574,3211,3213],{"className":3212},[625,626],[574,3214,3216],{"className":3215},[630],[574,3217,3219],{"className":3218},[634],[574,3220,3222,3230],{"className":3221,"style":621},[638],[574,3223,3224,3227],{"style":641},[574,3225],{"className":3226,"style":646},[645],[574,3228,599],{"className":3229},[625,650],[574,3231,3232,3235],{"style":641},[574,3233],{"className":3234,"style":646},[645],[574,3236,3238],{"className":3237,"style":660},[659],[574,3239,3241],{"className":3240,"style":665},[664],[667,3242,3243],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,3244],{"d":678},[574,3246],{"className":3247,"style":1149},[1148],[574,3249,3172],{"className":3250},[1153],[574,3252],{"className":3253,"style":1149},[1148],[574,3255,3257,3261,3339,3342,3377],{"className":3256},[616],[574,3258],{"className":3259,"style":3260},[620],"height:1.0894em;vertical-align:-0.3394em;",[574,3262,3264,3270],{"className":3263},[1315],[574,3265,3267],{"className":3266},[1315],[574,3268,555],{"className":3269},[625,1322],[574,3271,3273],{"className":3272},[1326],[574,3274,3276,3331],{"className":3275},[630,1171],[574,3277,3279,3328],{"className":3278},[634],[574,3280,3282],{"className":3281,"style":1336},[638],[574,3283,3284,3287],{"style":1339},[574,3285],{"className":3286,"style":1343},[645],[574,3288,3290],{"className":3289},[1188,1189,1190,1191],[574,3291,3293],{"className":3292},[625,1191],[574,3294,3296],{"className":3295},[625,626,1191],[574,3297,3299],{"className":3298},[630],[574,3300,3302],{"className":3301},[634],[574,3303,3305,3313],{"className":3304,"style":711},[638],[574,3306,3307,3310],{"style":1216},[574,3308],{"className":3309,"style":1220},[645],[574,3311,696],{"className":3312},[625,650,1191],[574,3314,3315,3318],{"style":1226},[574,3316],{"className":3317,"style":1220},[645],[574,3319,3321],{"className":3320,"style":660},[659],[574,3322,3324],{"className":3323,"style":665},[664,1191],[667,3325,3326],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,3327],{"d":678},[574,3329,1389],{"className":3330},[1388],[574,3332,3334],{"className":3333},[634],[574,3335,3337],{"className":3336,"style":1396},[638],[574,3338],{},[574,3340,1006],{"className":3341},[1402],[574,3343,3345],{"className":3344},[625,626],[574,3346,3348],{"className":3347},[630],[574,3349,3351],{"className":3350},[634],[574,3352,3354,3362],{"className":3353,"style":621},[638],[574,3355,3356,3359],{"style":641},[574,3357],{"className":3358,"style":646},[645],[574,3360,599],{"className":3361},[625,650],[574,3363,3364,3367],{"style":641},[574,3365],{"className":3366,"style":646},[645],[574,3368,3370],{"className":3369,"style":660},[659],[574,3371,3373],{"className":3372,"style":665},[664],[667,3374,3375],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,3376],{"d":678},[574,3378,1015],{"className":3379},[1441]," ist linear und idempotent: Zweimal projizieren ändert nichts mehr.",[2599,3382,3383,3384,3610,3611,3613,3614,3678,3679,3707,3708,1097],{},"Der Rest ",[574,3385,3387,3431],{"className":3386},[577],[574,3388,3390],{"className":3389},[581],[583,3391,3392],{"xmlns":585},[587,3393,3394,3428],{},[590,3395,3396,3402,3404,3418,3420,3426],{},[593,3397,3398,3400],{"accent":595},[597,3399,599],{},[601,3401,603],{},[601,3403,1053],{},[987,3405,3406,3412],{},[590,3407,3408,3410],{},[597,3409,555],{"mathvariant":993},[601,3411,996],{},[593,3413,3414,3416],{"accent":595},[597,3415,696],{},[601,3417,603],{},[601,3419,1006],{"stretchy":1005},[593,3421,3422,3424],{"accent":595},[597,3423,599],{},[601,3425,603],{},[601,3427,1015],{"stretchy":1005},[605,3429,3430],{"encoding":607},"\\vec{a} - \\operatorname{proj}_{\\vec{b}}(\\vec{a})",[574,3432,3434,3485],{"className":3433,"ariaHidden":595},[612],[574,3435,3437,3441,3476,3479,3482],{"className":3436},[616],[574,3438],{"className":3439,"style":3440},[620],"height:0.7973em;vertical-align:-0.0833em;",[574,3442,3444],{"className":3443},[625,626],[574,3445,3447],{"className":3446},[630],[574,3448,3450],{"className":3449},[634],[574,3451,3453,3461],{"className":3452,"style":621},[638],[574,3454,3455,3458],{"style":641},[574,3456],{"className":3457,"style":646},[645],[574,3459,599],{"className":3460},[625,650],[574,3462,3463,3466],{"style":641},[574,3464],{"className":3465,"style":646},[645],[574,3467,3469],{"className":3468,"style":660},[659],[574,3470,3472],{"className":3471,"style":665},[664],[667,3473,3474],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,3475],{"d":678},[574,3477],{"className":3478,"style":1469},[1148],[574,3480,1053],{"className":3481},[1473],[574,3483],{"className":3484,"style":1469},[1148],[574,3486,3488,3491,3569,3572,3607],{"className":3487},[616],[574,3489],{"className":3490,"style":3260},[620],[574,3492,3494,3500],{"className":3493},[1315],[574,3495,3497],{"className":3496},[1315],[574,3498,555],{"className":3499},[625,1322],[574,3501,3503],{"className":3502},[1326],[574,3504,3506,3561],{"className":3505},[630,1171],[574,3507,3509,3558],{"className":3508},[634],[574,3510,3512],{"className":3511,"style":1336},[638],[574,3513,3514,3517],{"style":1339},[574,3515],{"className":3516,"style":1343},[645],[574,3518,3520],{"className":3519},[1188,1189,1190,1191],[574,3521,3523],{"className":3522},[625,1191],[574,3524,3526],{"className":3525},[625,626,1191],[574,3527,3529],{"className":3528},[630],[574,3530,3532],{"className":3531},[634],[574,3533,3535,3543],{"className":3534,"style":711},[638],[574,3536,3537,3540],{"style":1216},[574,3538],{"className":3539,"style":1220},[645],[574,3541,696],{"className":3542},[625,650,1191],[574,3544,3545,3548],{"style":1226},[574,3546],{"className":3547,"style":1220},[645],[574,3549,3551],{"className":3550,"style":660},[659],[574,3552,3554],{"className":3553,"style":665},[664,1191],[667,3555,3556],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,3557],{"d":678},[574,3559,1389],{"className":3560},[1388],[574,3562,3564],{"className":3563},[634],[574,3565,3567],{"className":3566,"style":1396},[638],[574,3568],{},[574,3570,1006],{"className":3571},[1402],[574,3573,3575],{"className":3574},[625,626],[574,3576,3578],{"className":3577},[630],[574,3579,3581],{"className":3580},[634],[574,3582,3584,3592],{"className":3583,"style":621},[638],[574,3585,3586,3589],{"style":641},[574,3587],{"className":3588,"style":646},[645],[574,3590,599],{"className":3591},[625,650],[574,3593,3594,3597],{"style":641},[574,3595],{"className":3596,"style":646},[645],[574,3598,3600],{"className":3599,"style":660},[659],[574,3601,3603],{"className":3602,"style":665},[664],[667,3604,3605],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,3606],{"d":678},[574,3608,1015],{"className":3609},[1441]," ist der ",[569,3612,554],{},". Seine Länge ist der Abstand der Spitze von ",[574,3615,3617,3634],{"className":3616},[577],[574,3618,3620],{"className":3619},[581],[583,3621,3622],{"xmlns":585},[587,3623,3624,3632],{},[590,3625,3626],{},[593,3627,3628,3630],{"accent":595},[597,3629,599],{},[601,3631,603],{},[605,3633,608],{"encoding":607},[574,3635,3637],{"className":3636,"ariaHidden":595},[612],[574,3638,3640,3643],{"className":3639},[616],[574,3641],{"className":3642,"style":621},[620],[574,3644,3646],{"className":3645},[625,626],[574,3647,3649],{"className":3648},[630],[574,3650,3652],{"className":3651},[634],[574,3653,3655,3663],{"className":3654,"style":621},[638],[574,3656,3657,3660],{"style":641},[574,3658],{"className":3659,"style":646},[645],[574,3661,599],{"className":3662},[625,650],[574,3664,3665,3668],{"style":641},[574,3666],{"className":3667,"style":646},[645],[574,3669,3671],{"className":3670,"style":660},[659],[574,3672,3674],{"className":3673,"style":665},[664],[667,3675,3676],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,3677],{"d":678}," zur Geraden durch ",[574,3680,3682,3695],{"className":3681},[577],[574,3683,3685],{"className":3684},[581],[583,3686,3687],{"xmlns":585},[587,3688,3689,3693],{},[590,3690,3691],{},[2167,3692,2169],{},[605,3694,2169],{"encoding":607},[574,3696,3698],{"className":3697,"ariaHidden":595},[612],[574,3699,3701,3704],{"className":3700},[616],[574,3702],{"className":3703,"style":2343},[620],[574,3705,2169],{"className":3706},[625]," in Richtung ",[574,3709,3711,3728],{"className":3710},[577],[574,3712,3714],{"className":3713},[581],[583,3715,3716],{"xmlns":585},[587,3717,3718,3726],{},[590,3719,3720],{},[593,3721,3722,3724],{"accent":595},[597,3723,696],{},[601,3725,603],{},[605,3727,701],{"encoding":607},[574,3729,3731],{"className":3730,"ariaHidden":595},[612],[574,3732,3734,3737],{"className":3733},[616],[574,3735],{"className":3736,"style":711},[620],[574,3738,3740],{"className":3739},[625,626],[574,3741,3743],{"className":3742},[630],[574,3744,3746],{"className":3745},[634],[574,3747,3749,3757],{"className":3748,"style":711},[638],[574,3750,3751,3754],{"style":641},[574,3752],{"className":3753,"style":646},[645],[574,3755,696],{"className":3756},[625,650],[574,3758,3759,3762],{"style":734},[574,3760],{"className":3761,"style":646},[645],[574,3763,3765],{"className":3764,"style":660},[659],[574,3766,3768],{"className":3767,"style":665},[664],[667,3769,3770],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,3771],{"d":678},[2599,3773,3774,3775,3778],{},"Das ",[569,3776,3777],{},"Gram-Schmidt-Verfahren"," zieht schrittweise solche Projektionen ab, um eine Orthogonalbasis zu bauen.",[565,3780,3781,3782,3846],{},"Die Formel gilt in jedem ",[574,3783,3785,3805],{"className":3784},[577],[574,3786,3788],{"className":3787},[581],[583,3789,3790],{"xmlns":585},[587,3791,3792,3802],{},[590,3793,3794],{},[3795,3796,3797,3799],"msup",{},[597,3798,829],{"mathvariant":828},[597,3800,3801],{},"n",[605,3803,3804],{"encoding":607},"\\mathbb{R}^n",[574,3806,3808],{"className":3807,"ariaHidden":595},[612],[574,3809,3811,3815],{"className":3810},[616],[574,3812],{"className":3813,"style":3814},[620],"height:0.6889em;",[574,3816,3818,3821],{"className":3817},[625],[574,3819,829],{"className":3820},[625,851],[574,3822,3824],{"className":3823},[1326],[574,3825,3827],{"className":3826},[630],[574,3828,3830],{"className":3829},[634],[574,3831,3834],{"className":3832,"style":3833},[638],"height:0.6644em;",[574,3835,3837,3840],{"style":3836},"top:-3.063em;margin-right:0.05em;",[574,3838],{"className":3839,"style":1343},[645],[574,3841,3843],{"className":3842},[1188,1189,1190,1191],[574,3844,3801],{"className":3845},[625,650,1191]," und allgemein in Räumen mit Skalarprodukt.",[560,3848,3850],{"id":3849},"beispiele","Beispiele",[565,3852,3853,3854,3993,3994,4127,4128,3993,4273,4418],{},"Für ",[574,3855,3857,3900],{"className":3856},[577],[574,3858,3860],{"className":3859},[581],[583,3861,3862],{"xmlns":585},[587,3863,3864,3897],{},[590,3865,3866,3872,3874,3876,3879,3882,3885,3888,3890,3892,3895],{},[593,3867,3868,3870],{"accent":595},[597,3869,599],{},[601,3871,603],{},[601,3873,978],{},[601,3875,1006],{"stretchy":1005},[2167,3877,3878],{},"2",[601,3880,3881],{"separator":595},",",[1025,3883,3884],{}," ",[2167,3886,3887],{},"1",[601,3889,3881],{"separator":595},[1025,3891,3884],{},[2167,3893,3894],{},"3",[601,3896,1015],{"stretchy":1005},[605,3898,3899],{"encoding":607},"\\vec{a} = (2,\\ 1,\\ 3)",[574,3901,3903,3953],{"className":3902,"ariaHidden":595},[612],[574,3904,3906,3909,3944,3947,3950],{"className":3905},[616],[574,3907],{"className":3908,"style":621},[620],[574,3910,3912],{"className":3911},[625,626],[574,3913,3915],{"className":3914},[630],[574,3916,3918],{"className":3917},[634],[574,3919,3921,3929],{"className":3920,"style":621},[638],[574,3922,3923,3926],{"style":641},[574,3924],{"className":3925,"style":646},[645],[574,3927,599],{"className":3928},[625,650],[574,3930,3931,3934],{"style":641},[574,3932],{"className":3933,"style":646},[645],[574,3935,3937],{"className":3936,"style":660},[659],[574,3938,3940],{"className":3939,"style":665},[664],[667,3941,3942],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,3943],{"d":678},[574,3945],{"className":3946,"style":1149},[1148],[574,3948,978],{"className":3949},[1153],[574,3951],{"className":3952,"style":1149},[1148],[574,3954,3956,3959,3962,3965,3969,3972,3975,3978,3981,3984,3987,3990],{"className":3955},[616],[574,3957],{"className":3958,"style":2182},[620],[574,3960,1006],{"className":3961},[1402],[574,3963,3878],{"className":3964},[625],[574,3966,3881],{"className":3967},[3968],"mpunct",[574,3970,3884],{"className":3971},[1148],[574,3973],{"className":3974,"style":1815},[1148],[574,3976,3887],{"className":3977},[625],[574,3979,3881],{"className":3980},[3968],[574,3982,3884],{"className":3983},[1148],[574,3985],{"className":3986,"style":1815},[1148],[574,3988,3894],{"className":3989},[625],[574,3991,1015],{"className":3992},[1441]," und ",[574,3995,3997,4035],{"className":3996},[577],[574,3998,4000],{"className":3999},[581],[583,4001,4002],{"xmlns":585},[587,4003,4004,4032],{},[590,4005,4006,4012,4014,4016,4018,4020,4022,4024,4026,4028,4030],{},[593,4007,4008,4010],{"accent":595},[597,4009,696],{},[601,4011,603],{},[601,4013,978],{},[601,4015,1006],{"stretchy":1005},[2167,4017,3887],{},[601,4019,3881],{"separator":595},[1025,4021,3884],{},[2167,4023,3887],{},[601,4025,3881],{"separator":595},[1025,4027,3884],{},[2167,4029,2169],{},[601,4031,1015],{"stretchy":1005},[605,4033,4034],{"encoding":607},"\\vec{b} = (1,\\ 1,\\ 0)",[574,4036,4038,4088],{"className":4037,"ariaHidden":595},[612],[574,4039,4041,4044,4079,4082,4085],{"className":4040},[616],[574,4042],{"className":4043,"style":711},[620],[574,4045,4047],{"className":4046},[625,626],[574,4048,4050],{"className":4049},[630],[574,4051,4053],{"className":4052},[634],[574,4054,4056,4064],{"className":4055,"style":711},[638],[574,4057,4058,4061],{"style":641},[574,4059],{"className":4060,"style":646},[645],[574,4062,696],{"className":4063},[625,650],[574,4065,4066,4069],{"style":734},[574,4067],{"className":4068,"style":646},[645],[574,4070,4072],{"className":4071,"style":660},[659],[574,4073,4075],{"className":4074,"style":665},[664],[667,4076,4077],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,4078],{"d":678},[574,4080],{"className":4081,"style":1149},[1148],[574,4083,978],{"className":4084},[1153],[574,4086],{"className":4087,"style":1149},[1148],[574,4089,4091,4094,4097,4100,4103,4106,4109,4112,4115,4118,4121,4124],{"className":4090},[616],[574,4092],{"className":4093,"style":2182},[620],[574,4095,1006],{"className":4096},[1402],[574,4098,3887],{"className":4099},[625],[574,4101,3881],{"className":4102},[3968],[574,4104,3884],{"className":4105},[1148],[574,4107],{"className":4108,"style":1815},[1148],[574,4110,3887],{"className":4111},[625],[574,4113,3881],{"className":4114},[3968],[574,4116,3884],{"className":4117},[1148],[574,4119],{"className":4120,"style":1815},[1148],[574,4122,2169],{"className":4123},[625],[574,4125,1015],{"className":4126},[1441]," ist ",[574,4129,4131,4161],{"className":4130},[577],[574,4132,4134],{"className":4133},[581],[583,4135,4136],{"xmlns":585},[587,4137,4138,4158],{},[590,4139,4140,4146,4148,4154,4156],{},[593,4141,4142,4144],{"accent":595},[597,4143,599],{},[601,4145,603],{},[601,4147,1852],{},[593,4149,4150,4152],{"accent":595},[597,4151,696],{},[601,4153,603],{},[601,4155,978],{},[2167,4157,3894],{},[605,4159,4160],{"encoding":607},"\\vec{a} \\cdot \\vec{b} = 3",[574,4162,4164,4214,4264],{"className":4163,"ariaHidden":595},[612],[574,4165,4167,4170,4205,4208,4211],{"className":4166},[616],[574,4168],{"className":4169,"style":621},[620],[574,4171,4173],{"className":4172},[625,626],[574,4174,4176],{"className":4175},[630],[574,4177,4179],{"className":4178},[634],[574,4180,4182,4190],{"className":4181,"style":621},[638],[574,4183,4184,4187],{"style":641},[574,4185],{"className":4186,"style":646},[645],[574,4188,599],{"className":4189},[625,650],[574,4191,4192,4195],{"style":641},[574,4193],{"className":4194,"style":646},[645],[574,4196,4198],{"className":4197,"style":660},[659],[574,4199,4201],{"className":4200,"style":665},[664],[667,4202,4203],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,4204],{"d":678},[574,4206],{"className":4207,"style":1469},[1148],[574,4209,1852],{"className":4210},[1473],[574,4212],{"className":4213,"style":1469},[1148],[574,4215,4217,4220,4255,4258,4261],{"className":4216},[616],[574,4218],{"className":4219,"style":711},[620],[574,4221,4223],{"className":4222},[625,626],[574,4224,4226],{"className":4225},[630],[574,4227,4229],{"className":4228},[634],[574,4230,4232,4240],{"className":4231,"style":711},[638],[574,4233,4234,4237],{"style":641},[574,4235],{"className":4236,"style":646},[645],[574,4238,696],{"className":4239},[625,650],[574,4241,4242,4245],{"style":734},[574,4243],{"className":4244,"style":646},[645],[574,4246,4248],{"className":4247,"style":660},[659],[574,4249,4251],{"className":4250,"style":665},[664],[667,4252,4253],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,4254],{"d":678},[574,4256],{"className":4257,"style":1149},[1148],[574,4259,978],{"className":4260},[1153],[574,4262],{"className":4263,"style":1149},[1148],[574,4265,4267,4270],{"className":4266},[616],[574,4268],{"className":4269,"style":2343},[620],[574,4271,3894],{"className":4272},[625],[574,4274,4276,4306],{"className":4275},[577],[574,4277,4279],{"className":4278},[581],[583,4280,4281],{"xmlns":585},[587,4282,4283,4303],{},[590,4284,4285,4291,4293,4299,4301],{},[593,4286,4287,4289],{"accent":595},[597,4288,696],{},[601,4290,603],{},[601,4292,1852],{},[593,4294,4295,4297],{"accent":595},[597,4296,696],{},[601,4298,603],{},[601,4300,978],{},[2167,4302,3878],{},[605,4304,4305],{"encoding":607},"\\vec{b} \\cdot \\vec{b} = 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,4627,3894],{},[601,4629,1015],{"fence":595},[605,4631,4632],{"encoding":607},"\\operatorname{proj}_{\\vec{b}}(\\vec{a}) = \\frac{3}{2} \\begin{pmatrix} 1 \\\\ 1 \\\\ 0 \\end{pmatrix} = \\begin{pmatrix} \\frac{3}{2} \\\\ \\frac{3}{2} \\\\ 0 \\end{pmatrix},\n\\qquad\n\\vec{a} - \\operatorname{proj}_{\\vec{b}}(\\vec{a}) = \\begin{pmatrix} \\frac{1}{2} \\\\ -\\frac{1}{2} \\\\ 3 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Die Projektion hat die Länge ",[574,6086,6088,6115],{"className":6087},[577],[574,6089,6091],{"className":6090},[581],[583,6092,6093],{"xmlns":585},[587,6094,6095,6112],{},[590,6096,6097,6106,6109],{},[1840,6098,6099,6101],{},[2167,6100,3894],{},[6102,6103,6104],"msqrt",{},[2167,6105,3878],{},[601,6107,6108],{},"≈",[2167,6110,6111],{},"2,12",[605,6113,6114],{"encoding":607},"\\frac{3}{\\sqrt{2}} \\approx 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von ",[574,6282,6284,6326],{"className":6283},[577],[574,6285,6287],{"className":6286},[581],[583,6288,6289],{"xmlns":585},[587,6290,6291,6323],{},[590,6292,6293,6299,6301,6303,6305,6307,6309,6311,6314,6316,6318,6321],{},[593,6294,6295,6297],{"accent":595},[597,6296,599],{},[601,6298,603],{},[601,6300,978],{},[601,6302,1006],{"stretchy":1005},[2167,6304,3894],{},[601,6306,3881],{"separator":595},[1025,6308,3884],{},[601,6310,1053],{},[2167,6312,6313],{},"4",[601,6315,3881],{"separator":595},[1025,6317,3884],{},[2167,6319,6320],{},"5",[601,6322,1015],{"stretchy":1005},[605,6324,6325],{"encoding":607},"\\vec{a} = (3,\\ -4,\\ 5)",[574,6327,6329,6379],{"className":6328,"ariaHidden":595},[612],[574,6330,6332,6335,6370,6373,6376],{"className":6331},[616],[574,6333],{"className":6334,"style":621},[620],[574,6336,6338],{"className":6337},[625,626],[574,6339,6341],{"className":6340},[630],[574,6342,6344],{"className":6343},[634],[574,6345,6347,6355],{"className":6346,"style":621},[638],[574,6348,6349,6352],{"style":641},[574,6350],{"className":6351,"style":646},[645],[574,6353,599],{"className":6354},[625,650],[574,6356,6357,6360],{"style":641},[574,6358],{"className":6359,"style":646},[645],[574,6361,6363],{"className":6362,"style":660},[659],[574,6364,6366],{"className":6365,"style":665},[664],[667,6367,6368],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,6369],{"d":678},[574,6371],{"className":6372,"style":1149},[1148],[574,6374,978],{"className":6375},[1153],[574,6377],{"className":6378,"style":1149},[1148],[574,6380,6382,6385,6388,6391,6394,6397,6400,6403,6406,6409,6412,6415,6418],{"className":6381},[616],[574,6383],{"className":6384,"style":2182},[620],[574,6386,1006],{"className":6387},[1402],[574,6389,3894],{"className":6390},[625],[574,6392,3881],{"className":6393},[3968],[574,6395,3884],{"className":6396},[1148],[574,6398],{"className":6399,"style":1815},[1148],[574,6401,1053],{"className":6402},[625],[574,6404,6313],{"className":6405},[625],[574,6407,3881],{"className":6408},[3968],[574,6410,3884],{"className":6411},[1148],[574,6413],{"className":6414,"style":1815},[1148],[574,6416,6320],{"className":6417},[625],[574,6419,1015],{"className":6420},[1441]," auf den Einheitsvektor ",[574,6423,6425,6463],{"className":6424},[577],[574,6426,6428],{"className":6427},[581],[583,6429,6430],{"xmlns":585},[587,6431,6432,6460],{},[590,6433,6434,6440,6442,6444,6446,6448,6450,6452,6454,6456,6458],{},[593,6435,6436,6438],{"accent":595},[597,6437,696],{},[601,6439,603],{},[601,6441,978],{},[601,6443,1006],{"stretchy":1005},[2167,6445,2169],{},[601,6447,3881],{"separator":595},[1025,6449,3884],{},[2167,6451,3887],{},[601,6453,3881],{"separator":595},[1025,6455,3884],{},[2167,6457,2169],{},[601,6459,1015],{"stretchy":1005},[605,6461,6462],{"encoding":607},"\\vec{b} = (0,\\ 1,\\ 0)",[574,6464,6466,6516],{"className":6465,"ariaHidden":595},[612],[574,6467,6469,6472,6507,6510,6513],{"className":6468},[616],[574,6470],{"className":6471,"style":711},[620],[574,6473,6475],{"className":6474},[625,626],[574,6476,6478],{"className":6477},[630],[574,6479,6481],{"className":6480},[634],[574,6482,6484,6492],{"className":6483,"style":711},[638],[574,6485,6486,6489],{"style":641},[574,6487],{"className":6488,"style":646},[645],[574,6490,696],{"className":6491},[625,650],[574,6493,6494,6497],{"style":734},[574,6495],{"className":6496,"style":646},[645],[574,6498,6500],{"className":6499,"style":660},[659],[574,6501,6503],{"className":6502,"style":665},[664],[667,6504,6505],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,6506],{"d":678},[574,6508],{"className":6509,"style":1149},[1148],[574,6511,978],{"className":6512},[1153],[574,6514],{"className":6515,"style":1149},[1148],[574,6517,6519,6522,6525,6528,6531,6534,6537,6540,6543,6546,6549,6552],{"className":6518},[616],[574,6520],{"className":6521,"style":2182},[620],[574,6523,1006],{"className":6524},[1402],[574,6526,2169],{"className":6527},[625],[574,6529,3881],{"className":6530},[3968],[574,6532,3884],{"className":6533},[1148],[574,6535],{"className":6536,"style":1815},[1148],[574,6538,3887],{"className":6539},[625],[574,6541,3881],{"className":6542},[3968],[574,6544,3884],{"className":6545},[1148],[574,6547],{"className":6548,"style":1815},[1148],[574,6550,2169],{"className":6551},[625],[574,6553,1015],{"className":6554},[1441],": Der Faktor ist ",[574,6557,6559,6591],{"className":6558},[577],[574,6560,6562],{"className":6561},[581],[583,6563,6564],{"xmlns":585},[587,6565,6566,6588],{},[590,6567,6568,6574,6576,6582,6584,6586],{},[593,6569,6570,6572],{"accent":595},[597,6571,599],{},[601,6573,603],{},[601,6575,1852],{},[593,6577,6578,6580],{"accent":595},[597,6579,696],{},[601,6581,603],{},[601,6583,978],{},[601,6585,1053],{},[2167,6587,6313],{},[605,6589,6590],{"encoding":607},"\\vec{a} \\cdot \\vec{b} = 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also ",[574,6709,6711,6769],{"className":6710},[577],[574,6712,6714],{"className":6713},[581],[583,6715,6716],{"xmlns":585},[587,6717,6718,6766],{},[590,6719,6720,6734,6736,6742,6744,6746,6748,6750,6752,6754,6756,6758,6760,6762,6764],{},[987,6721,6722,6728],{},[590,6723,6724,6726],{},[597,6725,555],{"mathvariant":993},[601,6727,996],{},[593,6729,6730,6732],{"accent":595},[597,6731,696],{},[601,6733,603],{},[601,6735,1006],{"stretchy":1005},[593,6737,6738,6740],{"accent":595},[597,6739,599],{},[601,6741,603],{},[601,6743,1015],{"stretchy":1005},[601,6745,978],{},[601,6747,1006],{"stretchy":1005},[2167,6749,2169],{},[601,6751,3881],{"separator":595},[1025,6753,3884],{},[601,6755,1053],{},[2167,6757,6313],{},[601,6759,3881],{"separator":595},[1025,6761,3884],{},[2167,6763,2169],{},[601,6765,1015],{"stretchy":1005},[605,6767,6768],{"encoding":607},"\\operatorname{proj}_{\\vec{b}}(\\vec{a}) = (0,\\ -4,\\ 0)",[574,6770,6772,6906],{"className":6771,"ariaHidden":595},[612],[574,6773,6775,6778,6856,6859,6894,6897,6900,6903],{"className":6774},[616],[574,6776],{"className":6777,"style":3260},[620],[574,6779,6781,6787],{"className":6780},[1315],[574,6782,6784],{"className":6783},[1315],[574,6785,555],{"className":6786},[625,1322],[574,6788,6790],{"className":6789},[1326],[574,6791,6793,6848],{"className":6792},[630,1171],[574,6794,6796,6845],{"className":6795},[634],[574,6797,6799],{"className":6798,"style":1336},[638],[574,6800,6801,6804],{"style":1339},[574,6802],{"className":6803,"style":1343},[645],[574,6805,6807],{"className":6806},[1188,1189,1190,1191],[574,6808,6810],{"className":6809},[625,1191],[574,6811,6813],{"className":6812},[625,626,1191],[574,6814,6816],{"className":6815},[630],[574,6817,6819],{"className":6818},[634],[574,6820,6822,6830],{"className":6821,"style":711},[638],[574,6823,6824,6827],{"style":1216},[574,6825],{"className":6826,"style":1220},[645],[574,6828,696],{"className":6829},[625,650,1191],[574,6831,6832,6835],{"style":1226},[574,6833],{"className":6834,"style":1220},[645],[574,6836,6838],{"className":6837,"style":660},[659],[574,6839,6841],{"className":6840,"style":665},[664,1191],[667,6842,6843],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,6844],{"d":678},[574,6846,1389],{"className":6847},[1388],[574,6849,6851],{"className":6850},[634],[574,6852,6854],{"className":6853,"style":1396},[638],[574,6855],{},[574,6857,1006],{"className":6858},[1402],[574,6860,6862],{"className":6861},[625,626],[574,6863,6865],{"className":6864},[630],[574,6866,6868],{"className":6867},[634],[574,6869,6871,6879],{"className":6870,"style":621},[638],[574,6872,6873,6876],{"style":641},[574,6874],{"className":6875,"style":646},[645],[574,6877,599],{"className":6878},[625,650],[574,6880,6881,6884],{"style":641},[574,6882],{"className":6883,"style":646},[645],[574,6885,6887],{"className":6886,"style":660},[659],[574,6888,6890],{"className":6889,"style":665},[664],[667,6891,6892],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,6893],{"d":678},[574,6895,1015],{"className":6896},[1441],[574,6898],{"className":6899,"style":1149},[1148],[574,6901,978],{"className":6902},[1153],[574,6904],{"className":6905,"style":1149},[1148],[574,6907,6909,6912,6915,6918,6921,6924,6927,6930,6933,6936,6939,6942,6945],{"className":6908},[616],[574,6910],{"className":6911,"style":2182},[620],[574,6913,1006],{"className":6914},[1402],[574,6916,2169],{"className":6917},[625],[574,6919,3881],{"className":6920},[3968],[574,6922,3884],{"className":6923},[1148],[574,6925],{"className":6926,"style":1815},[1148],[574,6928,1053],{"className":6929},[625],[574,6931,6313],{"className":6932},[625],[574,6934,3881],{"className":6935},[3968],[574,6937,3884],{"className":6938},[1148],[574,6940],{"className":6941,"style":1815},[1148],[574,6943,2169],{"className":6944},[625],[574,6946,1015],{"className":6947},[1441],". Bei Einheitsvektoren der Koordinatenachsen liest man die Projektion direkt ab.",[560,6950,6952],{"id":6951},"typische-fehler","Typische Fehler",[2596,6954,6955,7257,7597],{},[2599,6956,6957,6958,7033,7034,7256],{},"Durch ",[574,6959,6961,6983],{"className":6960},[577],[574,6962,6964],{"className":6963},[581],[583,6965,6966],{"xmlns":585},[587,6967,6968,6980],{},[590,6969,6970,6972,6978],{},[597,6971,2620],{"mathvariant":993},[593,6973,6974,6976],{"accent":595},[597,6975,696],{},[601,6977,603],{},[597,6979,2620],{"mathvariant":993},[605,6981,6982],{"encoding":607},"|\\vec{b}|",[574,6984,6986],{"className":6985,"ariaHidden":595},[612],[574,6987,6989,6992,6995,7030],{"className":6988},[616],[574,6990],{"className":6991,"style":2236},[620],[574,6993,2620],{"className":6994},[625],[574,6996,6998],{"className":6997},[625,626],[574,6999,7001],{"className":7000},[630],[574,7002,7004],{"className":7003},[634],[574,7005,7007,7015],{"className":7006,"style":711},[638],[574,7008,7009,7012],{"style":641},[574,7010],{"className":7011,"style":646},[645],[574,7013,696],{"className":7014},[625,650],[574,7016,7017,7020],{"style":734},[574,7018],{"className":7019,"style":646},[645],[574,7021,7023],{"className":7022,"style":660},[659],[574,7024,7026],{"className":7025,"style":665},[664],[667,7027,7028],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,7029],{"d":678},[574,7031,2620],{"className":7032},[625]," statt durch ",[574,7035,7037,7079],{"className":7036},[577],[574,7038,7040],{"className":7039},[581],[583,7041,7042],{"xmlns":585},[587,7043,7044,7076],{},[590,7045,7046,7048,7054,7060,7062,7068,7070],{},[597,7047,2620],{"mathvariant":993},[593,7049,7050,7052],{"accent":595},[597,7051,696],{},[601,7053,603],{},[3795,7055,7056,7058],{},[597,7057,2620],{"mathvariant":993},[2167,7059,3878],{},[601,7061,978],{},[593,7063,7064,7066],{"accent":595},[597,7065,696],{},[601,7067,603],{},[601,7069,1852],{},[593,7071,7072,7074],{"accent":595},[597,7073,696],{},[601,7075,603],{},[605,7077,7078],{"encoding":607},"|\\vec{b}|^2 = \\vec{b} \\cdot \\vec{b}",[574,7080,7082,7165,7215],{"className":7081,"ariaHidden":595},[612],[574,7083,7085,7088,7091,7126,7156,7159,7162],{"className":7084},[616],[574,7086],{"className":7087,"style":2236},[620],[574,7089,2620],{"className":7090},[625],[574,7092,7094],{"className":7093},[625,626],[574,7095,7097],{"className":7096},[630],[574,7098,7100],{"className":7099},[634],[574,7101,7103,7111],{"className":7102,"style":711},[638],[574,7104,7105,7108],{"style":641},[574,7106],{"className":7107,"style":646},[645],[574,7109,696],{"className":7110},[625,650],[574,7112,7113,7116],{"style":734},[574,7114],{"className":7115,"style":646},[645],[574,7117,7119],{"className":7118,"style":660},[659],[574,7120,7122],{"className":7121,"style":665},[664],[667,7123,7124],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,7125],{"d":678},[574,7127,7129,7132],{"className":7128},[625],[574,7130,2620],{"className":7131},[625],[574,7133,7135],{"className":7134},[1326],[574,7136,7138],{"className":7137},[630],[574,7139,7141],{"className":7140},[634],[574,7142,7145],{"className":7143,"style":7144},[638],"height:0.8141em;",[574,7146,7147,7150],{"style":3836},[574,7148],{"className":7149,"style":1343},[645],[574,7151,7153],{"className":7152},[1188,1189,1190,1191],[574,7154,3878],{"className":7155},[625,1191],[574,7157],{"className":7158,"style":1149},[1148],[574,7160,978],{"className":7161},[1153],[574,7163],{"className":7164,"style":1149},[1148],[574,7166,7168,7171,7206,7209,7212],{"className":7167},[616],[574,7169],{"className":7170,"style":711},[620],[574,7172,7174],{"className":7173},[625,626],[574,7175,7177],{"className":7176},[630],[574,7178,7180],{"className":7179},[634],[574,7181,7183,7191],{"className":7182,"style":711},[638],[574,7184,7185,7188],{"style":641},[574,7186],{"className":7187,"style":646},[645],[574,7189,696],{"className":7190},[625,650],[574,7192,7193,7196],{"style":734},[574,7194],{"className":7195,"style":646},[645],[574,7197,7199],{"className":7198,"style":660},[659],[574,7200,7202],{"className":7201,"style":665},[664],[667,7203,7204],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,7205],{"d":678},[574,7207],{"className":7208,"style":1469},[1148],[574,7210,1852],{"className":7211},[1473],[574,7213],{"className":7214,"style":1469},[1148],[574,7216,7218,7221],{"className":7217},[616],[574,7219],{"className":7220,"style":711},[620],[574,7222,7224],{"className":7223},[625,626],[574,7225,7227],{"className":7226},[630],[574,7228,7230],{"className":7229},[634],[574,7231,7233,7241],{"className":7232,"style":711},[638],[574,7234,7235,7238],{"style":641},[574,7236],{"className":7237,"style":646},[645],[574,7239,696],{"className":7240},[625,650],[574,7242,7243,7246],{"style":734},[574,7244],{"className":7245,"style":646},[645],[574,7247,7249],{"className":7248,"style":660},[659],[574,7250,7252],{"className":7251,"style":665},[664],[667,7253,7254],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,7255],{"d":678}," teilen. Das ist nur bei Einheitsvektoren dasselbe.",[2599,7258,7259,3993,7426,7596],{},[574,7260,7262,7298],{"className":7261},[577],[574,7263,7265],{"className":7264},[581],[583,7266,7267],{"xmlns":585},[587,7268,7269,7295],{},[590,7270,7271,7285,7287,7293],{},[987,7272,7273,7279],{},[590,7274,7275,7277],{},[597,7276,555],{"mathvariant":993},[601,7278,996],{},[593,7280,7281,7283],{"accent":595},[597,7282,696],{},[601,7284,603],{},[601,7286,1006],{"stretchy":1005},[593,7288,7289,7291],{"accent":595},[597,7290,599],{},[601,7292,603],{},[601,7294,1015],{"stretchy":1005},[605,7296,7297],{"encoding":607},"\\operatorname{proj}_{\\vec{b}}(\\vec{a})",[574,7299,7301],{"className":7300,"ariaHidden":595},[612],[574,7302,7304,7307,7385,7388,7423],{"className":7303},[616],[574,7305],{"className":7306,"style":3260},[620],[574,7308,7310,7316],{"className":7309},[1315],[574,7311,7313],{"className":7312},[1315],[574,7314,555],{"className":7315},[625,1322],[574,7317,7319],{"className":7318},[1326],[574,7320,7322,7377],{"className":7321},[630,1171],[574,7323,7325,7374],{"className":7324},[634],[574,7326,7328],{"className":7327,"style":1336},[638],[574,7329,7330,7333],{"style":1339},[574,7331],{"className":7332,"style":1343},[645],[574,7334,7336],{"className":7335},[1188,1189,1190,1191],[574,7337,7339],{"className":7338},[625,1191],[574,7340,7342],{"className":7341},[625,626,1191],[574,7343,7345],{"className":7344},[630],[574,7346,7348],{"className":7347},[634],[574,7349,7351,7359],{"className":7350,"style":711},[638],[574,7352,7353,7356],{"style":1216},[574,7354],{"className":7355,"style":1220},[645],[574,7357,696],{"className":7358},[625,650,1191],[574,7360,7361,7364],{"style":1226},[574,7362],{"className":7363,"style":1220},[645],[574,7365,7367],{"className":7366,"style":660},[659],[574,7368,7370],{"className":7369,"style":665},[664,1191],[667,7371,7372],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,7373],{"d":678},[574,7375,1389],{"className":7376},[1388],[574,7378,7380],{"className":7379},[634],[574,7381,7383],{"className":7382,"style":1396},[638],[574,7384],{},[574,7386,1006],{"className":7387},[1402],[574,7389,7391],{"className":7390},[625,626],[574,7392,7394],{"className":7393},[630],[574,7395,7397],{"className":7396},[634],[574,7398,7400,7408],{"className":7399,"style":621},[638],[574,7401,7402,7405],{"style":641},[574,7403],{"className":7404,"style":646},[645],[574,7406,599],{"className":7407},[625,650],[574,7409,7410,7413],{"style":641},[574,7411],{"className":7412,"style":646},[645],[574,7414,7416],{"className":7415,"style":660},[659],[574,7417,7419],{"className":7418,"style":665},[664],[667,7420,7421],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,7422],{"d":678},[574,7424,1015],{"className":7425},[1441],[574,7427,7429,7465],{"className":7428},[577],[574,7430,7432],{"className":7431},[581],[583,7433,7434],{"xmlns":585},[587,7435,7436,7462],{},[590,7437,7438,7452,7454,7460],{},[987,7439,7440,7446],{},[590,7441,7442,7444],{},[597,7443,555],{"mathvariant":993},[601,7445,996],{},[593,7447,7448,7450],{"accent":595},[597,7449,599],{},[601,7451,603],{},[601,7453,1006],{"stretchy":1005},[593,7455,7456,7458],{"accent":595},[597,7457,696],{},[601,7459,603],{},[601,7461,1015],{"stretchy":1005},[605,7463,7464],{"encoding":607},"\\operatorname{proj}_{\\vec{a}}(\\vec{b})",[574,7466,7468],{"className":7467,"ariaHidden":595},[612],[574,7469,7471,7474,7555,7558,7593],{"className":7470},[616],[574,7472],{"className":7473,"style":2236},[620],[574,7475,7477,7483],{"className":7476},[1315],[574,7478,7480],{"className":7479},[1315],[574,7481,555],{"className":7482},[625,1322],[574,7484,7486],{"className":7485},[1326],[574,7487,7489,7546],{"className":7488},[630,1171],[574,7490,7492,7543],{"className":7491},[634],[574,7493,7496],{"className":7494,"style":7495},[638],"height:0.2557em;",[574,7497,7499,7502],{"style":7498},"top:-2.4559em;margin-right:0.05em;",[574,7500],{"className":7501,"style":1343},[645],[574,7503,7505],{"className":7504},[1188,1189,1190,1191],[574,7506,7508],{"className":7507},[625,1191],[574,7509,7511],{"className":7510},[625,626,1191],[574,7512,7514],{"className":7513},[630],[574,7515,7517],{"className":7516},[634],[574,7518,7520,7528],{"className":7519,"style":621},[638],[574,7521,7522,7525],{"style":1216},[574,7523],{"className":7524,"style":1220},[645],[574,7526,599],{"className":7527},[625,650,1191],[574,7529,7530,7533],{"style":1216},[574,7531],{"className":7532,"style":1220},[645],[574,7534,7536],{"className":7535,"style":660},[659],[574,7537,7539],{"className":7538,"style":665},[664,1191],[667,7540,7541],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,7542],{"d":678},[574,7544,1389],{"className":7545},[1388],[574,7547,7549],{"className":7548},[634],[574,7550,7553],{"className":7551,"style":7552},[638],"height:0.2441em;",[574,7554],{},[574,7556,1006],{"className":7557},[1402],[574,7559,7561],{"className":7560},[625,626],[574,7562,7564],{"className":7563},[630],[574,7565,7567],{"className":7566},[634],[574,7568,7570,7578],{"className":7569,"style":711},[638],[574,7571,7572,7575],{"style":641},[574,7573],{"className":7574,"style":646},[645],[574,7576,696],{"className":7577},[625,650],[574,7579,7580,7583],{"style":734},[574,7581],{"className":7582,"style":646},[645],[574,7584,7586],{"className":7585,"style":660},[659],[574,7587,7589],{"className":7588,"style":665},[664],[667,7590,7591],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,7592],{"d":678},[574,7594,1015],{"className":7595},[1441]," verwechseln. Die Projektion ist nicht symmetrisch.",[2599,7598,7599,7600,7629,7630,7700,7701,1097],{},"Den Faktor ",[574,7601,7603,7617],{"className":7602},[577],[574,7604,7606],{"className":7605},[581],[583,7607,7608],{"xmlns":585},[587,7609,7610,7614],{},[590,7611,7612],{},[597,7613,1836],{},[605,7615,7616],{"encoding":607},"\\lambda",[574,7618,7620],{"className":7619,"ariaHidden":595},[612],[574,7621,7623,7626],{"className":7622},[616],[574,7624],{"className":7625,"style":1887},[620],[574,7627,1836],{"className":7628},[625,650]," als Ergebnis angeben. Die Projektion ist der Vektor ",[574,7631,7633,7653],{"className":7632},[577],[574,7634,7636],{"className":7635},[581],[583,7637,7638],{"xmlns":585},[587,7639,7640,7650],{},[590,7641,7642,7644],{},[597,7643,1836],{},[593,7645,7646,7648],{"accent":595},[597,7647,696],{},[601,7649,603],{},[605,7651,7652],{"encoding":607},"\\lambda \\vec{b}",[574,7654,7656],{"className":7655,"ariaHidden":595},[612],[574,7657,7659,7662,7665],{"className":7658},[616],[574,7660],{"className":7661,"style":711},[620],[574,7663,1836],{"className":7664},[625,650],[574,7666,7668],{"className":7667},[625,626],[574,7669,7671],{"className":7670},[630],[574,7672,7674],{"className":7673},[634],[574,7675,7677,7685],{"className":7676,"style":711},[638],[574,7678,7679,7682],{"style":641},[574,7680],{"className":7681,"style":646},[645],[574,7683,696],{"className":7684},[625,650],[574,7686,7687,7690],{"style":734},[574,7688],{"className":7689,"style":646},[645],[574,7691,7693],{"className":7692,"style":660},[659],[574,7694,7696],{"className":7695,"style":665},[664],[667,7697,7698],{"xmlns":669,"width":670,"height":671,"style":672,"viewBox":673,"preserveAspectRatio":674},[676,7699],{"d":678},", nicht die Zahl 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