Thread: Find parametric equations for the line

Question
Lsub1 : x=1+2t, y=2-t, z=4-2t
Lsub2 : x=9+t , y=5+3t, z=-4-t

Lsub1 and Lsub2 intersect at the point (7,-1,-2).

Find parametric equations for the line that is perpendicular to Lsub1 and Lsub2 passes through their point of intersection.

* if possible, please draw me the picture. I can't figure out how this line can perpendicular to Lsub1 and Lsub2.

Thank you very much.

Originally Posted by Jenny20

Question
Lsub1 : x=1+2t, y=2-t, z=4-2t
Lsub2 : x=9+t , y=5+3t, z=-4-t

Lsub1 and Lsub2 intersect at the point (7,-1,-2).

Find parametric equations for the line that is perpendicular to Lsub1 and Lsub2 passes through their point of intersection.

* if possible, please draw me the picture. I can't figure out how this line can perpendicular to Lsub1 and Lsub2.

Thank you very much.

Consider the xyz plane.
The x-axis and y-axis intersect.
And z-axis is perpendicular to both of them.
That is how the visuallization looks.

Line 1) Is algined with the vector,


Line 2) Is algined with vector,


The line that we seek is perpendicular to both, that is a vector that is orthogonal to both these non-zero vectors.

We can use the cross product,
.

We can remove the 7 multiple, because if it is algined with it is certainly aligned with .

Thus, the parametric equations are,