Chapter 11.5, Problem 55ES

Let $L_1\text{ and }{L}_2$ be the lines whose parametric equations are

$\begin{array}{l}{L}_1:x=1+2t,y=2-t,z=4-2t\\ L_2:x=9+t,y=5+3t,z=-4-t\end{array}$

(a) Show that $L_1\text{ and }{L}_2$ intersect at the point $\left(7,-1,-2\right).$

(b) Find, to the nearest degree, the acute angle between $L_1\text{ and }{L}_2$ at their intersection.

(c) Find parametric equations for the line that is perpendicular to $L_1\text{ and }{L}_2$ and passes through their point of intersection.