Let $Q(3, -2, 7)$ be a point and let $L$ be the line whose equation in vector form is $\langle x,y,z \rangle = \langle -2, 5, -3\rangle + t \langle 1, 2, -2 \rangle$.

a) Find the equation of the plane $P_1$ that contains $Q$ and $L$.
b) Find the equation of the plane $P_2$ that contains $Q$ and is orthogonal to $L$.
c) Find the equation of a line through $Q$ that is orthogonal to $P_2$.
d) Find the distance from $Q$ to $L$.
e) Find the equation of a line through $Q$ that intersects $L$. There are many possible answers (depending on where it hits $L$).
f) Find the equation of a line through $Q$ that does NOT intersect $L$. How do you know that the two lines don't intersect?

Stewart Section 12.5, pages 824-6, problems 22, 50, 68