Finding the intersection of a line with $x,y,z$ coordinate planes How do I find the points at which the line given by the symmetric equation:
$$
\frac{-x - 1}{-1} = \frac{y + 5}{2} = \frac{z - 6}{-3}
$$
intersects the coordinate planes $xz$, $yz$, $xy$?

One idea:
First write the line as parametric equations:
$$
\begin{align}
x &= -1 +t \\
y &= -5 + 2t \\
z &= 6 - 3t.
\end{align}
$$
You have intersection with $xy$-plane when $z=0$, so that gives $t=2$ which gives you the point of intersection $(1, -1, 0)$. Now do likewise for the other planes.
