Question

Find an equation of plane passing through the point (2,-3,1) and containing the line x-3=2y=3z-1

Answer 1

re-write the line equation as \[\left(\begin{matrix}x \\ y\\z\end{matrix}\right) = \left(\begin{matrix}3 \\ 0\\1/3\end{matrix}\right) + t\left(\begin{matrix}1 \\ 1/2 \\1/3\end{matrix}\right)\]

nb: i've posted these to give you an idea of what to do but do not rely on the actual numbers, check them first as they could easily be wrong....

then find 2 points on that line, say at t = 0, t = 1. you will then have 3 points in total which lie on the plane.

that is enough to solve.

from there i would calculate 2 direction vectors lying on the plane, and take a cross product to find the normal vector for the plane, then plug a point in to find the plane constant....

but you may have your own way to go from there.

hope this helped :p