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braucht ",[580,1189,1191,1216],{"className":1190},[583],[580,1192,1194],{"className":1193},[587],[589,1195,1196],{"xmlns":591},[593,1197,1198,1213],{},[596,1199,1200,1207,1211],{},[599,1201,1202,1205],{},[602,1203,1204],{},"u",[606,1206,752],{},[754,1208,1210],{"mathvariant":1209},"normal","≠",[606,1212,759],{},[617,1214,1215],{"encoding":619},"u_3 \\neq 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= 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= 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\\neq 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die passende Koordinate des Richtungsvektors ",[580,2147,2149,2162],{"className":2148},[583],[580,2150,2152],{"className":2151},[587],[589,2153,2154],{"xmlns":591},[593,2155,2156,2160],{},[596,2157,2158],{},[606,2159,759],{},[617,2161,759],{"encoding":619},[580,2163,2165],{"className":2164,"ariaHidden":625},[624],[580,2166,2168,2171],{"className":2167},[629],[580,2169],{"className":2170,"style":830},[633],[580,2172,759],{"className":2173},[638],", verläuft die Gerade parallel zu dieser Koordinatenebene. Dann gibt es keinen Spurpunkt, oder die Gerade liegt ganz in der Ebene, wenn auch die Koordinate des Stützvektors ",[580,2176,2178,2191],{"className":2177},[583],[580,2179,2181],{"className":2180},[587],[589,2182,2183],{"xmlns":591},[593,2184,2185,2189],{},[596,2186,2187],{},[606,2188,759],{},[617,2190,759],{"encoding":619},[580,2192,2194],{"className":2193,"ariaHidden":625},[624],[580,2195,2197,2200],{"className":2196},[629],[580,2198],{"className":2199,"style":830},[633],[580,2201,759],{"className":2202},[638]," 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\\vec{x} = \\begin{pmatrix} 2 \\\\ -1 \\\\ 4 \\end{pmatrix} + t \\cdot \\begin{pmatrix} 1 \\\\ 1 \\\\ -2 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hat keinen Spurpunkt in der ",[580,4092,4094,4117],{"className":4093},[583],[580,4095,4097],{"className":4096},[587],[589,4098,4099],{"xmlns":591},[593,4100,4101,4115],{},[596,4102,4103,4109],{},[599,4104,4105,4107],{},[602,4106,604],{},[606,4108,608],{},[599,4110,4111,4113],{},[602,4112,604],{},[606,4114,615],{},[617,4116,620],{"encoding":619},[580,4118,4120],{"className":4119,"ariaHidden":625},[624],[580,4121,4123,4126,4166],{"className":4122},[629],[580,4124],{"className":4125,"style":634},[633],[580,4127,4129,4132],{"className":4128},[638],[580,4130,604],{"className":4131},[638,642],[580,4133,4135],{"className":4134},[646],[580,4136,4138,4158],{"className":4137},[650,651],[580,4139,4141,4155],{"className":4140},[655],[580,4142,4144],{"className":4143,"style":660},[659],[580,4145,4146,4149],{"style":663},[580,4147],{"className":4148,"style":668},[667],[580,4150,4152],{"className":4151},[672,673,674,675],[580,4153,608],{"className":4154},[638,675],[580,4156,683],{"className":4157},[682],[580,4159,4161],{"className":4160},[655],[580,4162,4164],{"className":4163,"style":690},[659],[580,4165],{},[580,4167,4169,4172],{"className":4168},[638],[580,4170,604],{"className":4171},[638,642],[580,4173,4175],{"className":4174},[646],[580,4176,4178,4198],{"className":4177},[650,651],[580,4179,4181,4195],{"className":4180},[655],[580,4182,4184],{"className":4183,"style":660},[659],[580,4185,4186,4189],{"style":663},[580,4187],{"className":4188,"style":668},[667],[580,4190,4192],{"className":4191},[672,673,674,675],[580,4193,615],{"className":4194},[638,675],[580,4196,683],{"className":4197},[682],[580,4199,4201],{"className":4200},[655],[580,4202,4204],{"className":4203,"style":690},[659],[580,4205],{},"-Ebene: Die dritte Zeile ",[580,4208,4210,4236],{"className":4209},[583],[580,4211,4213],{"className":4212},[587],[589,4214,4215],{"xmlns":591},[593,4216,4217,4233],{},[596,4218,4219,4221,4223,4225,4227,4229,4231],{},[606,4220,752],{},[754,4222,2307],{},[606,4224,759],{},[754,4226,2312],{},[602,4228,849],{},[754,4230,756],{},[606,4232,759],{},[617,4234,4235],{"encoding":619},"3 + 0 \\cdot t = 0",[580,4237,4239,4257,4275,4293],{"className":4238,"ariaHidden":625},[624],[580,4240,4242,4245,4248,4251,4254],{"className":4241},[629],[580,4243],{"className":4244,"style":2914},[633],[580,4246,752],{"className":4247},[638],[580,4249],{"className":4250,"style":2627},[815],[580,4252,2307],{"className":4253},[2631],[580,4255],{"className":4256,"style":2627},[815],[580,4258,4260,4263,4266,4269,4272],{"className":4259},[629],[580,4261],{"className":4262,"style":830},[633],[580,4264,759],{"className":4265},[638],[580,4267],{"className":4268,"style":2627},[815],[580,4270,2312],{"className":4271},[2631],[580,4273],{"className":4274,"style":2627},[815],[580,4276,4278,4281,4284,4287,4290],{"className":4277},[629],[580,4279],{"className":4280,"style":861},[633],[580,4282,849],{"className":4283},[638,642],[580,4285],{"className":4286,"style":816},[815],[580,4288,756],{"className":4289},[820],[580,4291],{"className":4292,"style":816},[815],[580,4294,4296,4299],{"className":4295},[629],[580,4297],{"className":4298,"style":830},[633],[580,4300,759],{"className":4301},[638]," hat keine Lösung, ",[580,4304,4306,4319],{"className":4305},[583],[580,4307,4309],{"className":4308},[587],[589,4310,4311],{"xmlns":591},[593,4312,4313,4317],{},[596,4314,4315],{},[602,4316,3837],{},[617,4318,3837],{"encoding":619},[580,4320,4322],{"className":4321,"ariaHidden":625},[624],[580,4323,4325,4329],{"className":4324},[629],[580,4326],{"className":4327,"style":4328},[633],"height:0.6944em;",[580,4330,3837],{"className":4331},[638,642]," verläuft parallel zu dieser Ebene.",[559,4334,4336],{"id":4335},"typische-fehler","Typische Fehler",[896,4338,4339,4371,4722],{},[899,4340,4341,4342,4370],{},"Den Parameter ",[580,4343,4345,4358],{"className":4344},[583],[580,4346,4348],{"className":4347},[587],[589,4349,4350],{"xmlns":591},[593,4351,4352,4356],{},[596,4353,4354],{},[602,4355,849],{},[617,4357,849],{"encoding":619},[580,4359,4361],{"className":4360,"ariaHidden":625},[624],[580,4362,4364,4367],{"className":4363},[629],[580,4365],{"className":4366,"style":861},[633],[580,4368,849],{"className":4369},[638,642]," als Spurpunkt angeben. Erst das Einsetzen in die Geradengleichung liefert den Punkt.",[899,4372,4373,4374,733,4489,4580,4581,4651,4652,1324],{},"Die falsche Koordinate null setzen: In der ",[580,4375,4377,4400],{"className":4376},[583],[580,4378,4380],{"className":4379},[587],[589,4381,4382],{"xmlns":591},[593,4383,4384,4398],{},[596,4385,4386,4392],{},[599,4387,4388,4390],{},[602,4389,604],{},[606,4391,608],{},[599,4393,4394,4396],{},[602,4395,604],{},[606,4397,615],{},[617,4399,620],{"encoding":619},[580,4401,4403],{"className":4402,"ariaHidden":625},[624],[580,4404,4406,4409,4449],{"className":4405},[629],[580,4407],{"className":4408,"style":634},[633],[580,4410,4412,4415],{"className":4411},[638],[580,4413,604],{"className":4414},[638,642],[580,4416,4418],{"className":4417},[646],[580,4419,4421,4441],{"className":4420},[650,651],[580,4422,4424,4438],{"className":4423},[655],[580,4425,4427],{"className":4426,"style":660},[659],[580,4428,4429,4432],{"style":663},[580,4430],{"className":4431,"style":668},[667],[580,4433,4435],{"className":4434},[672,673,674,675],[580,4436,608],{"className":4437},[638,675],[580,4439,683],{"className":4440},[682],[580,4442,4444],{"className":4443},[655],[580,4445,4447],{"className":4446,"style":690},[659],[580,4448],{},[580,4450,4452,4455],{"className":4451},[638],[580,4453,604],{"className":4454},[638,642],[580,4456,4458],{"className":4457},[646],[580,4459,4461,4481],{"className":4460},[650,651],[580,4462,4464,4478],{"className":4463},[655],[580,4465,4467],{"className":4466,"style":660},[659],[580,4468,4469,4472],{"style":663},[580,4470],{"className":4471,"style":668},[667],[580,4473,4475],{"className":4474},[672,673,674,675],[580,4476,615],{"className":4477},[638,675],[580,4479,683],{"className":4480},[682],[580,4482,4484],{"className":4483},[655],[580,4485,4487],{"className":4486,"style":690},[659],[580,4488],{},[580,4490,4492,4513],{"className":4491},[583],[580,4493,4495],{"className":4494},[587],[589,4496,4497],{"xmlns":591},[593,4498,4499,4511],{},[596,4500,4501,4507,4509],{},[599,4502,4503,4505],{},[602,4504,604],{},[606,4506,752],{},[754,4508,756],{},[606,4510,759],{},[617,4512,762],{"encoding":619},[580,4514,4516,4571],{"className":4515,"ariaHidden":625},[624],[580,4517,4519,4522,4562,4565,4568],{"className":4518},[629],[580,4520],{"className":4521,"style":634},[633],[580,4523,4525,4528],{"className":4524},[638],[580,4526,604],{"className":4527},[638,642],[580,4529,4531],{"className":4530},[646],[580,4532,4534,4554],{"className":4533},[650,651],[580,4535,4537,4551],{"className":4536},[655],[580,4538,4540],{"className":4539,"style":660},[659],[580,4541,4542,4545],{"style":663},[580,4543],{"className":4544,"style":668},[667],[580,4546,4548],{"className":4547},[672,673,674,675],[580,4549,752],{"className":4550},[638,675],[580,4552,683],{"className":4553},[682],[580,4555,4557],{"className":4556},[655],[580,4558,4560],{"className":4559,"style":690},[659],[580,4561],{},[580,4563],{"className":4564,"style":816},[815],[580,4566,756],{"className":4567},[820],[580,4569],{"className":4570,"style":816},[815],[580,4572,4574,4577],{"className":4573},[629],[580,4575],{"className":4576,"style":830},[633],[580,4578,759],{"className":4579},[638],", nicht ",[580,4582,4584,4602],{"className":4583},[583],[580,4585,4587],{"className":4586},[587],[589,4588,4589],{"xmlns":591},[593,4590,4591,4599],{},[596,4592,4593],{},[599,4594,4595,4597],{},[602,4596,604],{},[606,4598,608],{},[617,4600,4601],{"encoding":619},"x_1",[580,4603,4605],{"className":4604,"ariaHidden":625},[624],[580,4606,4608,4611],{"className":4607},[629],[580,4609],{"className":4610,"style":634},[633],[580,4612,4614,4617],{"className":4613},[638],[580,4615,604],{"className":4616},[638,642],[580,4618,4620],{"className":4619},[646],[580,4621,4623,4643],{"className":4622},[650,651],[580,4624,4626,4640],{"className":4625},[655],[580,4627,4629],{"className":4628,"style":660},[659],[580,4630,4631,4634],{"style":663},[580,4632],{"className":4633,"style":668},[667],[580,4635,4637],{"className":4636},[672,673,674,675],[580,4638,608],{"className":4639},[638,675],[580,4641,683],{"className":4642},[682],[580,4644,4646],{"className":4645},[655],[580,4647,4649],{"className":4648,"style":690},[659],[580,4650],{}," oder ",[580,4653,4655,4673],{"className":4654},[583],[580,4656,4658],{"className":4657},[587],[589,4659,4660],{"xmlns":591},[593,4661,4662,4670],{},[596,4663,4664],{},[599,4665,4666,4668],{},[602,4667,604],{},[606,4669,615],{},[617,4671,4672],{"encoding":619},"x_2",[580,4674,4676],{"className":4675,"ariaHidden":625},[624],[580,4677,4679,4682],{"className":4678},[629],[580,4680],{"className":4681,"style":634},[633],[580,4683,4685,4688],{"className":4684},[638],[580,4686,604],{"className":4687},[638,642],[580,4689,4691],{"className":4690},[646],[580,4692,4694,4714],{"className":4693},[650,651],[580,4695,4697,4711],{"className":4696},[655],[580,4698,4700],{"className":4699,"style":660},[659],[580,4701,4702,4705],{"style":663},[580,4703],{"className":4704,"style":668},[667],[580,4706,4708],{"className":4707},[672,673,674,675],[580,4709,615],{"className":4710},[638,675],[580,4712,683],{"className":4713},[682],[580,4715,4717],{"className":4716},[655],[580,4718,4720],{"className":4719,"style":690},[659],[580,4721],{},[899,4723,4724,4725,4817],{},"Bei ",[580,4726,4728,4750],{"className":4727},[583],[580,4729,4731],{"className":4730},[587],[589,4732,4733],{"xmlns":591},[593,4734,4735,4747],{},[596,4736,4737,4743,4745],{},[599,4738,4739,4741],{},[602,4740,1204],{},[606,4742,752],{},[754,4744,756],{},[606,4746,759],{},[617,4748,4749],{"encoding":619},"u_3 = 0",[580,4751,4753,4808],{"className":4752,"ariaHidden":625},[624],[580,4754,4756,4759,4799,4802,4805],{"className":4755},[629],[580,4757],{"className":4758,"style":634},[633],[580,4760,4762,4765],{"className":4761},[638],[580,4763,1204],{"className":4764},[638,642],[580,4766,4768],{"className":4767},[646],[580,4769,4771,4791],{"className":4770},[650,651],[580,4772,4774,4788],{"className":4773},[655],[580,4775,4777],{"className":4776,"style":660},[659],[580,4778,4779,4782],{"style":663},[580,4780],{"className":4781,"style":668},[667],[580,4783,4785],{"className":4784},[672,673,674,675],[580,4786,752],{"className":4787},[638,675],[580,4789,683],{"className":4790},[682],[580,4792,4794],{"className":4793},[655],[580,4795,4797],{"className":4796,"style":690},[659],[580,4798],{},[580,4800],{"className":4801,"style":816},[815],[580,4803,756],{"className":4804},[820],[580,4806],{"className":4807,"style":816},[815],[580,4809,4811,4814],{"className":4810},[629],[580,4812],{"className":4813,"style":830},[633],[580,4815,759],{"className":4816},[638]," durch null teilen, statt zu erkennen, dass die Gerade parallel zur Ebene verläuft.",{"title":4819,"searchDepth":4820,"depth":4820,"links":4821},"",2,[4822,4823,4824],{"id":561,"depth":4820,"text":562},{"id":2206,"depth":4820,"text":2207},{"id":4335,"depth":4820,"text":4336},[4826,4829,4831,4833,4837,4839,4841,4845,4848,4850],{"lhs":4827,"rhs":759,"where":4828},"4 + t*(-2)",{"t":4820},{"lhs":4830,"rhs":2301},"2 + 2*1",{"lhs":4832,"rhs":608},"-1 + 2*1",{"lhs":4834,"rhs":759,"where":4835},"-1 + t*1",{"t":4836},1,{"lhs":4838,"rhs":752},"2 + 1*1",{"lhs":4840,"rhs":615},"4 + 1*(-2)",{"lhs":4842,"rhs":759,"where":4843},"2 + t*1",{"t":4844},-2,{"lhs":4846,"rhs":4847},"-1 + (-2)*1","-3",{"lhs":4849,"rhs":3714},"4 + (-2)*(-2)",{"lhs":4851,"rhs":759},"p3 + (-p3\u002Fu3)*u3","g\\colon \\vec{x} = \\vec{p} + t \\cdot \\vec{u},\\ u_3 \\neq 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>g\u003C\u002Fmi>\u003Cmspace>\u003C\u002Fmspace>\u003Cmspace width=\"0.1111em\"\u002F>\u003Cmo lspace=\"0em\" rspace=\"0.17em\">\u003C\u002Fmo>\u003Cmtext> ⁣\u003C\u002Fmtext>\u003Cmo lspace=\"0em\" rspace=\"0em\">:\u003C\u002Fmo>\u003Cmspace width=\"0.3333em\"\u002F>\u003Cmover accent=\"true\">\u003Cmi>x\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>=\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>p\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>t\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmover accent=\"true\">\u003Cmi>u\u003C\u002Fmi>\u003Cmo>⃗\u003C\u002Fmo>\u003C\u002Fmover>\u003Cmo separator=\"true\">,\u003C\u002Fmo>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">g\\colon \\vec{x} = \\vec{p} + t \\cdot 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style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.1522em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1\n-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59\nH213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359\nc-16-25.333-24-45-24-59z\"\u002F>\u003C\u002Fsvg>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan 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katex-accent\">\u003Cspan class=\"vlist-t\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.714em;\">\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan style=\"top:-3em;\">\u003Cspan class=\"pstrut\" style=\"height:3em;\">\u003C\u002Fspan>\u003Cspan class=\"accent-body\" style=\"left:-0.2077em;\">\u003Cspan class=\"katex-overlay\" style=\"height:0.714em;width:0.471em;\">\u003Csvg xmlns=\"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg\" width=\"0.471em\" height=\"0.714em\" style=\"width:0.471em\" viewBox=\"0 0 471 714\" preserveAspectRatio=\"xMinYMin\">\u003Cpath d=\"M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 5\n3.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 11\n10.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63\n-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 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class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">3\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">\u003Cspan class=\"mrel\">\u003Cspan class=\"mord katex-vbox\">\u003Cspan class=\"katex-thinbox\">\u003Cspan class=\"rlap\">\u003Cspan class=\"katex-strut\" style=\"height:0.8889em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-inner\">\u003Cspan class=\"mord\">\u003Cspan class=\"mrel\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-fix\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace nobreak\">\u003C\u002Fspan>\u003Cspan class=\"mrel\">=\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mspace\" style=\"margin-right:0.2778em;\">\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"katex-base\">\u003Cspan class=\"katex-strut\" style=\"height:0.6444em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">0\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",null,"md","trace-points","S_{12}\\colon\\ p_3 + t \\cdot u_3 = 0 \\;\\Rightarrow\\; t = 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width=\"0.3333em\"\u002F>\u003Cmtext> \u003C\u002Fmtext>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>+\u003C\u002Fmo>\u003Cmi>t\u003C\u002Fmi>\u003Cmo>⋅\u003C\u002Fmo>\u003Cmsub>\u003Cmi>u\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmo>=\u003C\u002Fmo>\u003Cmn>0\u003C\u002Fmn>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmo>⇒\u003C\u002Fmo>\u003Cmtext>  \u003C\u002Fmtext>\u003Cmi>t\u003C\u002Fmi>\u003Cmo>=\u003C\u002Fmo>\u003Cmo>−\u003C\u002Fmo>\u003Cmfrac>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsub>\u003Cmsub>\u003Cmi>u\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmfrac>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">S_{12}\\colon\\ p_3 + t \\cdot u_3 = 0 \\;\\Rightarrow\\; t = -\\frac{p_3}{u_3}\u003C\u002Fannotation>\u003C\u002Fsemantics>\u003C\u002Fmath>\u003C\u002Fspan>\u003Cspan class=\"katex-html\" aria-hidden=\"true\">\u003Cspan 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style=\"height:0.836em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003Cspan class=\"mclose nulldelimiter\">\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","upper",{},true,"\u002Fde\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fspurpunkte-gerade",[],[4865,4866,4867],"line-parametric-form","plane-coordinate-form","vector-between-points",{"title":548,"description":4819},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fspurpunkte-gerade","Spurpunkte sind die Schnittpunkte einer Geraden mit den Koordinatenebenen; man setzt die passende Koordinate null.",[4872,4873,4874,4875],"spurpunkt","gerade","koordinatenebene","analytische geometrie",[4877,4880,4884,4888],{"symbol":923,"meaning":4878,"symbolHtml":4879},"Spurpunkt in der x₁x₂-Ebene, also der Punkt der Geraden mit x₃ = 0","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>S\u003C\u002Fmi>\u003Cmn>12\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">S_{12}\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:0.8333em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\" style=\"margin-right:0.0576em;\">S\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">\u003Cspan class=\"mord mtight\">12\u003C\u002Fspan>\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4881,"meaning":4882,"symbolHtml":4883},"p_3","dritte Koordinate des Stützvektors","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>p\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">p_3\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:0.625em;vertical-align:-0.1944em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">p\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">3\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":4885,"meaning":4886,"symbolHtml":4887},"u_3","dritte Koordinate des Richtungsvektors","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmsub>\u003Cmi>u\u003C\u002Fmi>\u003Cmn>3\u003C\u002Fmn>\u003C\u002Fmsub>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">u_3\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:0.5806em;vertical-align:-0.15em;\">\u003C\u002Fspan>\u003Cspan class=\"mord\">\u003Cspan class=\"mord mathnormal\">u\u003C\u002Fspan>\u003Cspan class=\"msupsub\">\u003Cspan class=\"vlist-t vlist-t2\">\u003Cspan class=\"vlist-r\">\u003Cspan class=\"vlist\" style=\"height:0.3011em;\">\u003Cspan style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\">\u003Cspan class=\"pstrut\" style=\"height:2.7em;\">\u003C\u002Fspan>\u003Cspan class=\"katex-sizing reset-size6 size3 mtight\">\u003Cspan class=\"mord mtight\">3\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:0.15em;\">\u003Cspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>",{"symbol":849,"meaning":4889,"symbolHtml":4890},"Parameterwert, der in die Geradengleichung eingesetzt den Spurpunkt liefert","\u003Cspan class=\"katex\">\u003Cspan class=\"katex-mathml\">\u003Cmath xmlns=\"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML\">\u003Csemantics>\u003Cmrow>\u003Cmi>t\u003C\u002Fmi>\u003C\u002Fmrow>\u003Cannotation encoding=\"application\u002Fx-tex\">t\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:0.6151em;\">\u003C\u002Fspan>\u003Cspan class=\"mord mathnormal\">t\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>\u003C\u002Fspan>","rw34DF9Nf7n7qkCGS8WDl_FNoztZcvHrWwDaD44pssQ",[4893,4896,4899],{"stem":4894,"title":4895,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fkoordinatenform-ebene","Koordinatenform einer Ebene",{"stem":4897,"title":4898,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fparameterform-gerade","Parameterform einer Geraden",{"stem":4900,"title":4901,"category":312},"de\u002Fformulas\u002Fmath\u002Flinear-algebra\u002Fverbindungsvektor","Verbindungsvektor",1793824280243]