Question

Find the equation of the plane which contains the line of intersection of the planes

vector r.(i+2j+3k) -4 =0 vector r.(2i+j-k)+5=0

vector r.(5i+3j-6k)+8=0 and which is perpendicular to the plane

Answer 1

The equations of the given planes are

The equation of the plane passing through the line intersection of the plane given in equation (1) and equation (2) is

The plane in equation (3) is perpendicular to the plane, 

This is the vector equation of the required plane.
The Cartesian equation of this plane can be obtained by substituting in equation (3).