TITLE: Find the equation of the plane that contains
QUESTION [6 upvotes]: Find the equation of the plane that contains,
the lines: $$
\frac{x-2}{2} = \frac{y+4}{3} = \frac{2 - z}{5}
$$
and
$$\begin{align}
x &= 3 + 4t \\
y &= -4 +6t \\
z &= 5 -10t.
\end{align}
$$
I'm not exactly sure on how to tackle this problem.

REPLY [2 votes]: Hints: To find a plane all you need is a point and a normal vector. You can get one point from one line.
The normal vector $n$ needs to be perpendicular on both lines, thus perpendicular on both their directions. How do you find a vector perpendicular on two given directions?