I'm trying to solve the following problem to no avail: Let bbr_1(t)=⟨8,−5,1⟩+t⟨0,−1,−4⟩ and bbr_2(s)=⟨12,−3,5⟩+s⟨1,0,−1⟩. Find the point of intersection, P, of the two lines bbr_1 and bbr_2.

tizamazg

tizamazg

Open question

2022-08-21

I'm trying to solve the following problem to no avail:
Let 𝐫 1 ( 𝑡 ) = 8 , 5 , 1 + 𝑡 0 , 1 , 4 and 𝐫 2 ( 𝑠 ) = 12 , 3 , 5 + 𝑠 1 , 0 , 1. Find the point of intersection, P, of the two lines 𝐫 1 and 𝐫 2
I've tried adding them together to their directional vectors, so r 1 ( t ) = 8 , 5 t , 1 4 t and r 2 12 + s , 3 , 5 1 s
Now would I like subtract them or something? I don't know what to do now.

Answer & Explanation

betoosolis7i

betoosolis7i

Beginner2022-08-22Added 12 answers

If you want to calculate the intersection, you have to solve the linear equation system
8 + 0 t = 12 + 1 s 5 1 t = 3 + 0 s 1 4 t = 5 1 s
for (t,s). Then plug one value into the corresponding line equation.

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