Question

Determine the equation of the line that is perpendicular to the lines r(t)=<4t,1+2t,3t> and R(s)=<-1+s,-7+2s,-12+3s> and passes through the point of intersection of the lines r and R.

Answer 1

I've already figured out the point of intersection (4,3,3) just not sure how to determine the perpendicular direction. I know I need to use cross product but how do I do that with two different variables??

Answer 2

use the "direction vectors" of each line e.g. for r(t), use <4,2,3>
and form the cross product. the result will be a vector perpendicular to both lines.

Answer 3

Ok so the perpendicular vector is <0,-9,6>. Thank you!

Answer 4

Well the answer to the question as a whole would be r(t)=<4,3,3>+t<0,-3,2>. Right?

Answer 5

yes, that is correct.