How can I calculate the basic vectors? How can I correctly think about this question?

PROBLEM 12. Consider the plane :3 y + z = 0. a) Find the 3 x 3 matrix P1 which represents projection of R3 onto a vector orthogonal to this plane. 1 b) Let 11' = 1 . Find vectors 2? and \"(If such that 11' = 17 + 117, where 17 is in the plane and ii} is 1 perpendicular to the plane. c) Find the 3 X 3 matrix P2 which represents the projection of R3 onto the given plane