Find symmetric equations for the line through (4, -11, -7)
that is parallel to the line x = 2+5t, y = −1+ 1
3 t, z = 9−2t.
and
Find parametric equations for the line through (2, -2, 15)
that is parallel to the xz-plane and the xy-plane.
I broke the given line down into its original form (r1 plus t x the direction vector). It's clearly the direction vector that the line must be parallel to. I have the r1 vector and the point given in the prompt, but I'm not sure what to do next.
As for the second one, I figured I would want to take it as the line parallel to the line of intersection of the two planes, which would be the x-axis. Is this the right way to look at it? If so, what then?