Question

The two line with equations L1: r = (1,2,-4) + t(k+1,3k+1,k-3) and L2: x=2-3s, y=1-10s, z=3-5s are given. a. determine the value of k if this lines are parallel. I tried to solved this but the correct answer is only -7, my answer is: k+1 = -3 -> -4 3k+1 = -10 -> -11/3 k-3 = -5 -> -2 because I took the t(k+1,3k+1,k-3) as tv(vector) and since it had to be parallel with the line, I took the vector from the other equation x=2-3s, y=1-10s, z=3-5s, which is -3,-10,-5 and i equated to the respective x y z in the first line...

Answer 1

L1: r = (1,2,-4) + t(k+1,3k+1,k-3)
L2: x=2-3s, y=1-10s, z=3-5s

if the ratio of the vector parts are equal, they are parallel

Answer 2

k+1 3k+1 k-3
-3 -10 -5

Answer 3

id prolly start by multiplying it all by -30 to get

10(k+1) = 3(3k+1) = 6(k-3)

Answer 4

or, (same idea, really)

(k+1,3k+1,k-3)*a = (-3 , -10 , -5)

solve for both a and k

Answer 5

wait let me try..

Answer 6

I got it thank you very much!