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Es ist ",[582,1072,1074,1120],{"className":1073},[585],[582,1075,1077],{"className":1076},[589],[591,1078,1079],{"xmlns":593},[595,1080,1081,1117],{},[598,1082,1083,1093,1096,1098,1100,1103,1107,1109,1111,1113,1115],{},[601,1084,1085,1091],{"accent":603},[598,1086,1087,1089],{},[607,1088,609],{},[607,1090,612],{},[614,1092,616],{"stretchy":603},[614,1094,1095],{},"=",[614,1097,805],{"stretchy":804},[807,1099,820],{},[614,1101,1102],{"separator":603},",",[1104,1105,1106],"mtext",{}," ",[807,1108,820],{},[614,1110,1102],{"separator":603},[1104,1112,1106],{},[807,1114,815],{},[614,1116,823],{"stretchy":804},[618,1118,1119],{"encoding":620},"\\overrightarrow{AB} = (2,\\ 2,\\ 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= (0,\\ 4,\\ 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an einem rechtwinkligen Dreieck mit ",[582,2481,2483,2511],{"className":2482},[585],[582,2484,2486],{"className":2485},[589],[591,2487,2488],{"xmlns":593},[595,2489,2490,2508],{},[598,2491,2492,2494,2496,2498,2500,2502,2504,2506],{},[607,2493,609],{},[614,2495,805],{"stretchy":804},[807,2497,815],{},[614,2499,812],{},[807,2501,815],{},[614,2503,812],{},[807,2505,815],{},[614,2507,823],{"stretchy":804},[618,2509,2510],{"encoding":620},"A(0 \\mid 0 \\mid 0)",[582,2512,2514,2538,2556],{"className":2513,"ariaHidden":603},[625],[582,2515,2517,2520,2523,2526,2529,2532,2535],{"className":2516},[629],[582,2518],{"className":2519,"style":836},[633],[582,2521,609],{"className":2522},[638,666],[582,2524,805],{"className":2525},[843],[582,2527,815],{"className":2528},[638],[582,2530],{"className":2531,"style":851},[850],[582,2533,812],{"className":2534},[855],[582,2536],{"className":2537,"style":851},[850],[582,2539,2541,2544,2547,2550,2553],{"className":2540},[629],[582,2542],{"className":2543,"style":836},[633],[582,2545,815],{"className":2546},[638],[582,2548],{"className":2549,"style":851},[850],[582,2551,812],{"className":2552},[855],[582,2554],{"className":2555,"style":851},[850],[582,2557,2559,2562,2565],{"className":2558},[629],[582,2560],{"className":2561,"style":836},[633],[582,2563,815],{"className":2564},[638],[582,2566,823],{"className":2567},[889],[582,2569,2571,2599],{"className":2570},[585],[582,2572,2574],{"className":2573},[589],[591,2575,2576],{"xmlns":593},[595,2577,2578,2596],{},[598,2579,2580,2582,2584,2586,2588,2590,2592,2594],{},[607,2581,612],{},[614,2583,805],{"stretchy":804},[807,2585,1002],{},[614,2587,812],{},[807,2589,815],{},[614,2591,812],{},[807,2593,815],{},[614,2595,823],{"stretchy":804},[618,2597,2598],{"encoding":620},"B(4 \\mid 0 \\mid 0)",[582,2600,2602,2626,2644],{"className":2601,"ariaHidden":603},[625],[582,2603,2605,2608,2611,2614,2617,2620,2623],{"className":2604},[629],[582,2606],{"className":2607,"style":836},[633],[582,2609,612],{"className":2610,"style":670},[638,666],[582,2612,805],{"className":2613},[843],[582,2615,1002],{"className":2616},[638],[582,2618],{"className":2619,"style":851},[850],[582,2621,812],{"className":2622},[855],[582,2624],{"className":2625,"style":851},[850],[582,2627,2629,2632,2635,2638,2641],{"className":2628},[629],[582,2630],{"className":2631,"style":836},[633],[582,2633,815],{"className":2634},[638],[582,2636],{"className":2637,"style":851},[850],[582,2639,812],{"className":2640},[855],[582,2642],{"className":2643,"style":851},[850],[582,2645,2647,2650,2653],{"className":2646},[629],[582,2648],{"className":2649,"style":836},[633],[582,2651,815],{"className":2652},[638],[582,2654,823],{"className":2655},[889],[582,2657,2659,2687],{"className":2658},[585],[582,2660,2662],{"className":2661},[589],[591,2663,2664],{"xmlns":593},[595,2665,2666,2684],{},[598,2667,2668,2670,2672,2674,2676,2678,2680,2682],{},[607,2669,717],{},[614,2671,805],{"stretchy":804},[807,2673,815],{},[614,2675,812],{},[807,2677,909],{},[614,2679,812],{},[807,2681,815],{},[614,2683,823],{"stretchy":804},[618,2685,2686],{"encoding":620},"C(0 \\mid 3 \\mid 0)",[582,2688,2690,2714,2732],{"className":2689,"ariaHidden":603},[625],[582,2691,2693,2696,2699,2702,2705,2708,2711],{"className":2692},[629],[582,2694],{"className":2695,"style":836},[633],[582,2697,717],{"className":2698,"style":758},[638,666],[582,2700,805],{"className":2701},[843],[582,2703,815],{"className":2704},[638],[582,2706],{"className":2707,"style":851},[850],[582,2709,812],{"className":2710},[855],[582,2712],{"className":2713,"style":851},[850],[582,2715,2717,2720,2723,2726,2729],{"className":2716},[629],[582,2718],{"className":2719,"style":836},[633],[582,2721,909],{"className":2722},[638],[582,2724],{"className":2725,"style":851},[850],[582,2727,812],{"className":2728},[855],[582,2730],{"className":2731,"style":851},[850],[582,2733,2735,2738,2741],{"className":2734},[629],[582,2736],{"className":2737,"style":836},[633],[582,2739,815],{"className":2740},[638],[582,2742,823],{"className":2743},[889],": Das Kreuzprodukt ist ",[582,2746,2748,2779],{"className":2747},[585],[582,2749,2751],{"className":2750},[589],[591,2752,2753],{"xmlns":593},[595,2754,2755,2776],{},[598,2756,2757,2759,2761,2763,2765,2767,2769,2771,2774],{},[614,2758,805],{"stretchy":804},[807,2760,815],{},[614,2762,1102],{"separator":603},[1104,2764,1106],{},[807,2766,815],{},[614,2768,1102],{"separator":603},[1104,2770,1106],{},[807,2772,2773],{},"12",[614,2775,823],{"stretchy":804},[618,2777,2778],{"encoding":620},"(0,\\ 0,\\ 12)",[582,2780,2782],{"className":2781,"ariaHidden":603},[625],[582,2783,2785,2788,2791,2794,2797,2800,2803,2806,2809,2812,2815,2818],{"className":2784},[629],[582,2786],{"className":2787,"style":836},[633],[582,2789,805],{"className":2790},[843],[582,2792,815],{"className":2793},[638],[582,2795,1102],{"className":2796},[1192],[582,2798,1106],{"className":2799},[850],[582,2801],{"className":2802,"style":1199},[850],[582,2804,815],{"className":2805},[638],[582,2807,1102],{"className":2808},[1192],[582,2810,1106],{"className":2811},[850],[582,2813],{"className":2814,"style":1199},[850],[582,2816,2773],{"className":2817},[638],[582,2819,823],{"className":2820},[889],", also ",[582,2823,2825,2843],{"className":2824},[585],[582,2826,2828],{"className":2827},[589],[591,2829,2830],{"xmlns":593},[595,2831,2832,2840],{},[598,2833,2834,2836,2838],{},[607,2835,2090],{},[614,2837,1095],{},[807,2839,1501],{},[618,2841,2842],{"encoding":620},"F = 6",[582,2844,2846,2864],{"className":2845,"ariaHidden":603},[625],[582,2847,2849,2852,2855,2858,2861],{"className":2848},[629],[582,2850],{"className":2851,"style":2149},[633],[582,2853,2090],{"className":2854,"style":2153},[638,666],[582,2856],{"className":2857,"style":851},[850],[582,2859,1095],{"className":2860},[855],[582,2862],{"className":2863,"style":851},[850],[582,2865,2867,2871],{"className":2866},[629],[582,2868],{"className":2869,"style":2870},[633],"height:0.6444em;",[582,2872,1501],{"className":2873},[638],". Das stimmt mit ",[582,2876,2878,2908],{"className":2877},[585],[582,2879,2881],{"className":2880},[589],[591,2882,2883],{"xmlns":593},[595,2884,2885,2905],{},[598,2886,2887,2893,2895,2897,2899,2901,2903],{},[2094,2888,2889,2891],{},[807,2890,809],{},[807,2892,820],{},[614,2894,1427],{},[807,2896,1002],{},[614,2898,1427],{},[807,2900,909],{},[614,2902,1095],{},[807,2904,1501],{},[618,2906,2907],{"encoding":620},"\\frac{1}{2} \\cdot 4 \\cdot 3 = 6",[582,2909,2911,3003,3021,3039],{"className":2910,"ariaHidden":603},[625],[582,2912,2914,2918,2994,2997,3000],{"className":2913},[629],[582,2915],{"className":2916,"style":2917},[633],"height:1.1901em;vertical-align:-0.345em;",[582,2919,2921,2924,2991],{"className":2920},[638],[582,2922],{"className":2923},[843,2176],[582,2925,2927],{"className":2926},[2094],[582,2928,2930,2982],{"className":2929},[643,1664],[582,2931,2933,2979],{"className":2932},[647],[582,2934,2937,2956,2964],{"className":2935,"style":2936},[651],"height:0.8451em;",[582,2938,2940,2943],{"style":2939},"top:-2.655em;",[582,2941],{"className":2942,"style":659},[658],[582,2944,2950],{"className":2945},[2946,2947,2948,2949],"sizing","reset-size6","size3","mtight",[582,2951,2953],{"className":2952},[638,2949],[582,2954,820],{"className":2955},[638,2949],[582,2957,2958,2961],{"style":2204},[582,2959],{"className":2960,"style":659},[658],[582,2962],{"className":2963,"style":2212},[2211],[582,2965,2967,2970],{"style":2966},"top:-3.394em;",[582,2968],{"className":2969,"style":659},[658],[582,2971,2973],{"className":2972},[2946,2947,2948,2949],[582,2974,2976],{"className":2975},[638,2949],[582,2977,809],{"className":2978},[638,2949],[582,2980,1694],{"className":2981},[1693],[582,2983,2985],{"className":2984},[647],[582,2986,2989],{"className":2987,"style":2988},[651],"height:0.345em;",[582,2990],{},[582,2992],{"className":2993},[889,2176],[582,2995],{"className":2996,"style":1580},[850],[582,2998,1427],{"className":2999},[1584],[582,3001],{"className":3002,"style":1580},[850],[582,3004,3006,3009,3012,3015,3018],{"className":3005},[629],[582,3007],{"className":3008,"style":2870},[633],[582,3010,1002],{"className":3011},[638],[582,3013],{"className":3014,"style":1580},[850],[582,3016,1427],{"className":3017},[1584],[582,3019],{"className":3020,"style":1580},[850],[582,3022,3024,3027,3030,3033,3036],{"className":3023},[629],[582,3025],{"className":3026,"style":2870},[633],[582,3028,909],{"className":3029},[638],[582,3031],{"className":3032,"style":851},[850],[582,3034,1095],{"className":3035},[855],[582,3037],{"className":3038,"style":851},[850],[582,3040,3042,3045],{"className":3041},[629],[582,3043],{"className":3044,"style":2870},[633],[582,3046,1501],{"className":3047},[638]," überein.",[558,3050,3052],{"id":3051},"typische-fehler","Typische Fehler",[3054,3055,3056,3158,3708],"ul",{},[578,3057,3058,3059,3157],{},"Den Faktor ",[582,3060,3062,3080],{"className":3061},[585],[582,3063,3065],{"className":3064},[589],[591,3066,3067],{"xmlns":593},[595,3068,3069,3077],{},[598,3070,3071],{},[2094,3072,3073,3075],{},[807,3074,809],{},[807,3076,820],{},[618,3078,3079],{"encoding":620},"\\frac{1}{2}",[582,3081,3083],{"className":3082,"ariaHidden":603},[625],[582,3084,3086,3089],{"className":3085},[629],[582,3087],{"className":3088,"style":2917},[633],[582,3090,3092,3095,3154],{"className":3091},[638],[582,3093],{"className":3094},[843,2176],[582,3096,3098],{"className":3097},[2094],[582,3099,3101,3146],{"className":3100},[643,1664],[582,3102,3104,3143],{"className":3103},[647],[582,3105,3107,3121,3129],{"className":3106,"style":2936},[651],[582,3108,3109,3112],{"style":2939},[582,3110],{"className":3111,"style":659},[658],[582,3113,3115],{"className":3114},[2946,2947,2948,2949],[582,3116,3118],{"className":3117},[638,2949],[582,3119,820],{"className":3120},[638,2949],[582,3122,3123,3126],{"style":2204},[582,3124],{"className":3125,"style":659},[658],[582,3127],{"className":3128,"style":2212},[2211],[582,3130,3131,3134],{"style":2966},[582,3132],{"className":3133,"style":659},[658],[582,3135,3137],{"className":3136},[2946,2947,2948,2949],[582,3138,3140],{"className":3139},[638,2949],[582,3141,809],{"className":3142},[638,2949],[582,3144,1694],{"className":3145},[1693],[582,3147,3149],{"className":3148},[647],[582,3150,3152],{"className":3151,"style":2988},[651],[582,3153],{},[582,3155],{"className":3156},[889,2176]," vergessen. Dann hat man die Fläche des Parallelogramms.",[578,3159,3160,3161,3413,3414,3442,3443,3669,3670,570],{},"Die Längen der Seitenvektoren multiplizieren. ",[582,3162,3164,3215],{"className":3163},[585],[582,3165,3167],{"className":3166},[589],[591,3168,3169],{"xmlns":593},[595,3170,3171,3212],{},[598,3172,3173,3179,3181,3184,3194,3196,3198,3200,3210],{},[2094,3174,3175,3177],{},[807,3176,809],{},[807,3178,820],{},[614,3180,1427],{},[607,3182,812],{"mathvariant":3183},"normal",[601,3185,3186,3192],{"accent":603},[598,3187,3188,3190],{},[607,3189,609],{},[607,3191,612],{},[614,3193,616],{"stretchy":603},[607,3195,812],{"mathvariant":3183},[614,3197,1427],{},[607,3199,812],{"mathvariant":3183},[601,3201,3202,3208],{"accent":603},[598,3203,3204,3206],{},[607,3205,609],{},[607,3207,717],{},[614,3209,616],{"stretchy":603},[607,3211,812],{"mathvariant":3183},[618,3213,3214],{"encoding":620},"\\frac{1}{2} \\cdot |\\overrightarrow{AB}| \\cdot |\\overrightarrow{AC}|",[582,3216,3218,3301,3362],{"className":3217,"ariaHidden":603},[625],[582,3219,3221,3224,3292,3295,3298],{"className":3220},[629],[582,3222],{"className":3223,"style":2917},[633],[582,3225,3227,3230,3289],{"className":3226},[638],[582,3228],{"className":3229},[843,2176],[582,3231,3233],{"className":3232},[2094],[582,3234,3236,3281],{"className":3235},[643,1664],[582,3237,3239,3278],{"className":3238},[647],[582,3240,3242,3256,3264],{"className":3241,"style":2936},[651],[582,3243,3244,3247],{"style":2939},[582,3245],{"className":3246,"style":659},[658],[582,3248,3250],{"className":3249},[2946,2947,2948,2949],[582,3251,3253],{"className":3252},[638,2949],[582,3254,820],{"className":3255},[638,2949],[582,3257,3258,3261],{"style":2204},[582,3259],{"className":3260,"style":659},[658],[582,3262],{"className":3263,"style":2212},[2211],[582,3265,3266,3269],{"style":2966},[582,3267],{"className":3268,"style":659},[658],[582,3270,3272],{"className":3271},[2946,2947,2948,2949],[582,3273,3275],{"className":3274},[638,2949],[582,3276,809],{"className":3277},[638,2949],[582,3279,1694],{"className":3280},[1693],[582,3282,3284],{"className":3283},[647],[582,3285,3287],{"className":3286,"style":2988},[651],[582,3288],{},[582,3290],{"className":3291},[889,2176],[582,3293],{"className":3294,"style":1580},[850],[582,3296,1427],{"className":3297},[1584],[582,3299],{"className":3300,"style":1580},[850],[582,3302,3304,3308,3311,3350,3353,3356,3359],{"className":3303},[629],[582,3305],{"className":3306,"style":3307},[633],"height:1.4553em;vertical-align:-0.25em;",[582,3309,812],{"className":3310},[638],[582,3312,3314],{"className":3313},[638,639],[582,3315,3317],{"className":3316},[643],[582,3318,3320],{"className":3319},[647],[582,3321,3323,3337],{"className":3322,"style":634},[651],[582,3324,3325,3328],{"style":654},[582,3326],{"className":3327,"style":659},[658],[582,3329,3331,3334],{"className":3330},[638],[582,3332,609],{"className":3333},[638,666],[582,3335,612],{"className":3336,"style":670},[638,666],[582,3338,3340,3343],{"className":3339,"style":675},[674],[582,3341],{"className":3342,"style":659},[658],[582,3344,3346],{"className":3345,"style":683},[682],[685,3347,3348],{"xmlns":687,"width":688,"height":689,"viewBox":690,"preserveAspectRatio":691},[693,3349],{"d":695},[582,3351,812],{"className":3352},[638],[582,3354],{"className":3355,"style":1580},[850],[582,3357,1427],{"className":3358},[1584],[582,3360],{"className":3361,"style":1580},[850],[582,3363,3365,3368,3371,3410],{"className":3364},[629],[582,3366],{"className":3367,"style":3307},[633],[582,3369,812],{"className":3370},[638],[582,3372,3374],{"className":3373},[638,639],[582,3375,3377],{"className":3376},[643],[582,3378,3380],{"className":3379},[647],[582,3381,3383,3397],{"className":3382,"style":634},[651],[582,3384,3385,3388],{"style":654},[582,3386],{"className":3387,"style":659},[658],[582,3389,3391,3394],{"className":3390},[638],[582,3392,609],{"className":3393},[638,666],[582,3395,717],{"className":3396,"style":758},[638,666],[582,3398,3400,3403],{"className":3399,"style":675},[674],[582,3401],{"className":3402,"style":659},[658],[582,3404,3406],{"className":3405,"style":683},[682],[685,3407,3408],{"xmlns":687,"width":688,"height":689,"viewBox":690,"preserveAspectRatio":691},[693,3409],{"d":695},[582,3411,812],{"className":3412},[638]," stimmt nur bei einem rechten Winkel in ",[582,3415,3417,3430],{"className":3416},[585],[582,3418,3420],{"className":3419},[589],[591,3421,3422],{"xmlns":593},[595,3423,3424,3428],{},[598,3425,3426],{},[607,3427,609],{},[618,3429,609],{"encoding":620},[582,3431,3433],{"className":3432,"ariaHidden":603},[625],[582,3434,3436,3439],{"className":3435},[629],[582,3437],{"className":3438,"style":2149},[633],[582,3440,609],{"className":3441},[638,666],". Im ersten Beispiel käme ",[582,3444,3446,3479],{"className":3445},[585],[582,3447,3449],{"className":3448},[589],[591,3450,3451],{"xmlns":593},[595,3452,3453,3476],{},[598,3454,3455,3461,3463,3467,3469,3471,3473],{},[2094,3456,3457,3459],{},[807,3458,809],{},[807,3460,820],{},[614,3462,1427],{},[2101,3464,3465],{},[807,3466,1522],{},[614,3468,1427],{},[807,3470,1007],{},[614,3472,2133],{},[807,3474,3475],{},"7,07",[618,3477,3478],{"encoding":620},"\\frac{1}{2} \\cdot \\sqrt{8} \\cdot 5 \\approx 7{,}07",[582,3480,3482,3565,3631,3649],{"className":3481,"ariaHidden":603},[625],[582,3483,3485,3488,3556,3559,3562],{"className":3484},[629],[582,3486],{"className":3487,"style":2917},[633],[582,3489,3491,3494,3553],{"className":3490},[638],[582,3492],{"className":3493},[843,2176],[582,3495,3497],{"className":3496},[2094],[582,3498,3500,3545],{"className":3499},[643,1664],[582,3501,3503,3542],{"className":3502},[647],[582,3504,3506,3520,3528],{"className":3505,"style":2936},[651],[582,3507,3508,3511],{"style":2939},[582,3509],{"className":3510,"style":659},[658],[582,3512,3514],{"className":3513},[2946,2947,2948,2949],[582,3515,3517],{"className":3516},[638,2949],[582,3518,820],{"className":3519},[638,2949],[582,3521,3522,3525],{"style":2204},[582,3523],{"className":3524,"style":659},[658],[582,3526],{"className":3527,"style":2212},[2211],[582,3529,3530,3533],{"style":2966},[582,3531],{"className":3532,"style":659},[658],[582,3534,3536],{"className":3535},[2946,2947,2948,2949],[582,3537,3539],{"className":3538},[638,2949],[582,3540,809],{"className":3541},[638,2949],[582,3543,1694],{"className":3544},[1693],[582,3546,3548],{"className":3547},[647],[582,3549,3551],{"className":3550,"style":2988},[651],[582,3552],{},[582,3554],{"className":3555},[889,2176],[582,3557],{"className":3558,"style":1580},[850],[582,3560,1427],{"className":3561},[1584],[582,3563],{"className":3564,"style":1580},[850],[582,3566,3568,3572,3622,3625,3628],{"className":3567},[629],[582,3569],{"className":3570,"style":3571},[633],"height:1.04em;vertical-align:-0.1328em;",[582,3573,3575],{"className":3574},[638,2243],[582,3576,3578,3613],{"className":3577},[643,1664],[582,3579,3581,3610],{"className":3580},[647],[582,3582,3585,3597],{"className":3583,"style":3584},[651],"height:0.9072em;",[582,3586,3588,3591],{"className":3587,"style":654},[674],[582,3589],{"className":3590,"style":659},[658],[582,3592,3594],{"className":3593,"style":2263},[638],[582,3595,1522],{"className":3596},[638],[582,3598,3600,3603],{"style":3599},"top:-2.8672em;",[582,3601],{"className":3602,"style":659},[658],[582,3604,3606],{"className":3605,"style":2300},[682],[685,3607,3608],{"xmlns":687,"width":688,"height":2303,"viewBox":2304,"preserveAspectRatio":2305},[693,3609],{"d":2308},[582,3611,1694],{"className":3612},[1693],[582,3614,3616],{"className":3615},[647],[582,3617,3620],{"className":3618,"style":3619},[651],"height:0.1328em;",[582,3621],{},[582,3623],{"className":3624,"style":1580},[850],[582,3626,1427],{"className":3627},[1584],[582,3629],{"className":3630,"style":1580},[850],[582,3632,3634,3637,3640,3643,3646],{"className":3633},[629],[582,3635],{"className":3636,"style":2870},[633],[582,3638,1007],{"className":3639},[638],[582,3641],{"className":3642,"style":851},[850],[582,3644,2133],{"className":3645},[855],[582,3647],{"className":3648,"style":851},[850],[582,3650,3652,3655,3659,3665],{"className":3651},[629],[582,3653],{"className":3654,"style":2463},[633],[582,3656,3658],{"className":3657},[638],"7",[582,3660,3662],{"className":3661},[638],[582,3663,1102],{"className":3664},[1192],[582,3666,3668],{"className":3667},[638],"07"," heraus statt ",[582,3671,3673,3687],{"className":3672},[585],[582,3674,3676],{"className":3675},[589],[591,3677,3678],{"xmlns":593},[595,3679,3680,3684],{},[598,3681,3682],{},[807,3683,2136],{},[618,3685,3686],{"encoding":620},"5{,}83",[582,3688,3690],{"className":3689,"ariaHidden":603},[625],[582,3691,3693,3696,3699,3705],{"className":3692},[629],[582,3694],{"className":3695,"style":2463},[633],[582,3697,1007],{"className":3698},[638],[582,3700,3702],{"className":3701},[638],[582,3703,1102],{"className":3704},[1192],[582,3706,2476],{"className":3707},[638],[578,3709,3710],{},"Ortsvektoren der Punkte statt Verbindungsvektoren verwenden.",{"title":3712,"searchDepth":3713,"depth":3713,"links":3714},"",2,[3715,3716,3717],{"id":560,"depth":3713,"text":561},{"id":783,"depth":3713,"text":784},{"id":3051,"depth":3713,"text":3052},[3719,3721,3723,3725,3727,3730,3732,3735,3738,3740,3742,3745,3747],{"lhs":3720,"rhs":820},"3 - 1",{"lhs":3722,"rhs":1002},"4 - 0",{"lhs":3724,"rhs":909},"5 - 2",{"lhs":3726,"rhs":1501},"2*3 - 0*4",{"lhs":3728,"rhs":3729},"0*0 - 2*3","-6",{"lhs":3731,"rhs":1522},"2*4 - 2*0",{"lhs":3733,"rhs":3734},"1\u002F2 * sqrt(6^2 + (-6)^2 + 8^2)","1\u002F2 * sqrt(136)",{"lhs":3736,"rhs":3737},"round(1\u002F2 * sqrt(136), 2)","5.83",{"lhs":3739,"rhs":1501},"1\u002F2 * abs(4*3 - 0*0)",{"lhs":3741,"rhs":1501},"1\u002F2 * 4 * 3",{"lhs":3743,"rhs":3744},"sqrt(2^2 + 2^2 + 0^2)","sqrt(8)",{"lhs":3746,"rhs":1007},"sqrt(0^2 + 4^2 + 3^2)",{"lhs":3748,"rhs":3749},"round(1\u002F2 * sqrt(8) * 5, 2)","7.07",null,"md","triangle-area-vectors","F = \\frac{1}{2} \\left|\\overrightarrow{AB} \\times \\overrightarrow{AC}\\right|","\u003Cspan class=\"katex-display\">\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\" display=\"block\">\u003Csemantics>\u003Cmrow>\u003Cmi>F\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmfrac>\u003Cmn>1\u003C\u002Fmn>\u003Cmn>2\u003C\u002Fmn>\u003C\u002Fmfrac>\u003Cmrow>\u003Cmo fence=\"true\">∣\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>B\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">→\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>×\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">→\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo fence=\"true\">∣\u003C\u002Fmo>\u003C\u002Fmrow>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">F = \\frac{1}{2} \\left|\\overrightarrow{AB} \\times \\overrightarrow{AC}\\right|\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:2.0074em;vertical-align:-0.686em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mopen nulldelimiter\">\u003C\u002Fspan>\u003Cspan class=\"mfrac\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.3214em;\">\u003Cspan style=\"top:-2.314em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">2\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.23em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"frac-line\" style=\"border-bottom-width:0.04em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3.677em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord\">1\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-s\">​\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.686em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"minner\">\u003Cspan class=\"mopen\">\u003Cspan class=\"delimsizing mult\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:1.15em;\">\u003Cspan 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style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"svg-align\" style=\"top:-3.6833em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"hide-tail\" style=\"height:0.522em;min-width:0.888em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"400em\" height=\"0.522em\" viewBox=\"0 0 400000 522\" preserveAspectRatio=\"xMaxYMin slice\">\u003Cpath d=\"M0 241v40h399891c-47.3 35.3-84 78-110 128\n-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20\n 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7\n 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85\n-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n 151.7 139 205zm0 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style=\"height:0.65em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fflaecheninhalt-dreieck-vektoren",[],[3761,3762,3763,3764],"parallelogram-area-vectors","cross-product","vector-between-points","triangle-area",{"title":548,"description":3712},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fflaecheninhalt-dreieck-vektoren","Der Flächeninhalt eines Dreiecks ist der halbe Betrag des Kreuzprodukts zweier Seitenvektoren.",[3769,3770,3771,3772],"dreieck","flächeninhalt","kreuzprodukt","vektor",[3774,3777,3781],{"symbol":2090,"meaning":3775,"symbolHtml":3776},"Flächeninhalt des Dreiecks","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>F\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">F\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6833em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.1389em;\">F\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3778,"meaning":3779,"symbolHtml":3780},"A, B, C","Eckpunkte des Dreiecks im Raum","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>B\u003C\u002Fmi>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">A, B, C\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">A\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0502em;\">B\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0715em;\">C\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":3782,"meaning":3783,"symbolHtml":3784},"\\overrightarrow{AB}, \\overrightarrow{AC}","Verbindungsvektoren von A zu den beiden anderen Ecken","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>B\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">→\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmrow>\u003Cmi>A\u003C\u002Fmi>\u003Cmi>C\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cmo stretchy=\"true\">→\u003C\u002Fmo>\u003C\u002Fmover>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">\\overrightarrow{AB}, 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xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"400em\" height=\"0.522em\" viewBox=\"0 0 400000 522\" preserveAspectRatio=\"xMaxYMin slice\">\u003Cpath d=\"M0 241v40h399891c-47.3 35.3-84 78-110 128\n-16.7 32-27.7 63.7-33 95 0 1.3-.2 2.7-.5 4-.3 1.3-.5 2.3-.5 3 0 7.3 6.7 11 20\n 11 8 0 13.2-.8 15.5-2.5 2.3-1.7 4.2-5.5 5.5-11.5 2-13.3 5.7-27 11-41 14.7-44.7\n 39-84.5 73-119.5s73.7-60.2 119-75.5c6-2 9-5.7 9-11s-3-9-9-11c-45.3-15.3-85\n-40.5-119-75.5s-58.3-74.8-73-119.5c-4.7-14-8.3-27.3-11-40-1.3-6.7-3.2-10.8-5.5\n-12.5-2.3-1.7-7.5-2.5-15.5-2.5-14 0-21 3.7-21 11 0 2 2 10.3 6 25 20.7 83.3 67\n 151.7 139 205zm0 0v40h399900v-40z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mpunct\">,\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.1667em;\">\u003C\u002Fspan>\u003Cspan class=\"mord katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan 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