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I want to solve

P0 + t0 * V0 + t2 * V2 == P1 + t1 * V1

for t0, t1 and t2, which are scalars, whereas the uppercase variables are three-dimensional constants.

I tried

solve[{P_0_0 + t_0 * V_0_0 + t_2 * V_2_0 == P_1_0 + t_1 * V_1_0, P_0_1 + t_0 * V_0_1 + t_2 * V_2_1 == P_1_1 + t_1 * V_1_1, P_0_2 + t_0 * V_0_2 + t_2 * V_2_2 == P_1_2 + t_1 * V_1_2}, {t_0, t_1, t_2}]

but Wolfram alpha doesn't understand the query.

How can I solve this linear system of equations using Wolfram Alpha?

matthias_buehlmann
  • 264
  • You may succeed if you give names to the three cordinates of each of the five upper case vectors, each of which as you say has three coordinates. Then you would have to determine what equations are implied when you "take coordinates" of your five vectors, and feed those into wolfram. Of course you'd have to somehow tell wolfram what were the constants, and the variables $t_k$ need to be told to wolfram so it knows what to solve for. [There may not be a solution for some values of the parameters, or more than one solution.] – coffeemath Nov 24 '21 at 16:02
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    You might want to try https://mathematica.stackexchange.com – PC1 Nov 24 '21 at 16:05

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