Question

Find the equation of the plane passing through (a, b, c) and parallel to the plane

Answer 1

Any plane parallel to the plane, , is of the form

The plane passes through the point (a, b, c). Therefore, the position vector of this point is

Therefore, equation (1) becomes

Substituting in equation (1), we obtain

This is the vector equation of the required plane.

Substituting in equation (2), we obtain