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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.

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  • $\begingroup$ 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 . $\endgroup$ Nov 30 '19 at 14:09
  • $\begingroup$ 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. $\endgroup$
    – amd
    Nov 30 '19 at 18:23
  • $\begingroup$ I know. But none of them seemed to make much sense to me... $\endgroup$
    – Human
    Dec 1 '19 at 17:36
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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

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

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

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