Question

L1:x=−2t,y=1+2t,z=3t and
L2:x=−9+5s,y=4+1s,z=3+3s
Find the point of intersection of the two lines.

Answer 1

set the components equal to each other and solve s, t

Answer 2

-2t = -9 + 5s ? like that?

Answer 3

Yes!

-2t = -9+5s
1+2t = 4+1s
3t = 3+3s

the lines will intersect if there is a solution to this system of 3 equations with 2 unknowns

Answer 4

OOH! that makes sense. Similar to finding intersection in 2-space.

Answer 5

going to try it out, thank you @ganeshie8

Answer 6

np :) you may simply pick any two equations and solve s,t

once you have s,t values plug them in the third equation and check if they satisfy

Answer 7

ah ok

Answer 8

woo got it, ty :)