Question

Find the equation of the plane that passes through the point P(-1,2,1) and contains the line of intersection of the planes x + y - z = 2 and 2x - y + 3z = 1

Answer 1

@alekos @amistre64 @dan815

Answer 2

any ideas ? My first thought is to find the equation of the line formed by the intersection of the 2 planes.

Answer 3

though I don't know what this means:
x + y -z z = 2

typo ?

Answer 4

I fixed it! How would I find the line?

Answer 5

any ideas how to get the direction vector of the line, using the normals of the planes?

Answer 6

Cross Product

Answer 7

yes. so use a cross product to find the direction vector.

also find a point that sits in both planes (so it will be on this line)
to do this, set z=0 and solve for x and y using the equations of the 2 planes. Call this point Q

Next create the vector from point Q to point P (i.e. P-Q)

you now have two direction vectors that lie in a plane parallel to the one you want.
cross product again to find its normal. Then use the fact that Q or P is in the plane to find the equation of the plane