## equation of plane

1. The problem statement, all variables and given/known data
Find the equation of the plane that passes throughthe point (-1,2,1) and contains the line of intersection of the planes x+y-z=2, and 2x-y+3=1

2. Relevant equations
$$a(x-x_{o})+b(y-y_{o})+c(z-z_{o})=0$$

3. The attempt at a solution
My reasoning is that we can take the normal vectors of the given planes, take the cross product, which will be orthoganol to the plane we want.
We then just plug the obtained normal vector and the point into the equation. Right?
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 that's correct
 Just wanted to check. I get an anwer but it is wrong from the books, so it must be my doing.

## equation of plane

 Shouldn't you find the the line of intersection? And then the direction from the point (-1,2,1) to a point on the line? And then find a vector perpendicular to the two directions? And then pick any point that you know is going to be on your plane to satisfy your scalar equations?

 Quote by ZioX Shouldn't you find the the line of intersection? And then the direction from the point (-1,2,1) to a point on the line? And then find a vector perpendicular to the two directions? And then pick any point that you know is going to be on your plane to satisfy your scalar equations?
yea thats right, i wasn't thinking straight. how do you find a vector that's perpindicular to the vector that points from the (-1,2,1) to the line of intersection? find a vector which when crossed with it = 0?

Mentor
 Quote by ice109 yea thats right, i wasn't thinking straight. how do you find a vector that's perpindicular to the vector that points from the (-1,2,1) to the line of intersection?
What is the angle between the cross product of two vectors and either of the two multiplicand vectors?

 Quote by D H What is the angle between the cross product of two vectors and either of the two multiplicand vectors?
90deg , yea just cross the vector from (-1,2,1) and the line of intersection to the normal vector of the plane