# Equation of plane

1. Jun 21, 2007

### Winzer

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?

2. Jun 21, 2007

### ice109

that's correct

3. Jun 21, 2007

### Winzer

Just wanted to check.
I get an anwer but it is wrong from the books, so it must be my doing.

4. Jun 21, 2007

### ice109

5. Jun 21, 2007

### 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?

6. Jun 22, 2007

### 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? find a vector which when crossed with it = 0?

7. Jun 22, 2007

### D H

Staff Emeritus
What is the angle between the cross product of two vectors and either of the two multiplicand vectors?

8. Jun 22, 2007

### ice109

90deg , yea just cross the vector from (-1,2,1) and the line of intersection to the normal vector of the plane