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

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.

• Welcome to Math SE! . Please read this How to ask a good question to begin with and share your thoughts and efforts in the question . Nov 30 '19 at 14:09
• Look through the handy list of related questions at right. There are at least two questions there about the same sort of problem as this one.
– amd
Nov 30 '19 at 18:23
• I know. But none of them seemed to make much sense to me... Dec 1 '19 at 17:36

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

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

• Wow. I solved it! I never tought it would be that simple! Dec 1 '19 at 17:35
• Sorry, by 'tought' I meant 'thought'. Dec 1 '19 at 17:35
• @Human Well done! That’s fine. Bye
– user
Dec 1 '19 at 17:39