Help on how to find an equation of a plane passing through a line and a point.

Question

My question is:

Find an equation for the plane that contains the point $(1, -1, 2)$ and the line $x=t, y=t+1, z=-3+2t$.

Can someone please give me a step-by-step explanation on how to do this? I have tried many ways, but none of them work.

Answer 1

HINT

We can proceed as follows

• take a vector $\vec v$ parallel to the line
• take a vector $\vec w$ form the given point to a point on the line

then a normal vector to the plane is given by

$$\vec n = \vec v \times \vec w$$