Find the matrix for the transformation that projects each point in R3 (3-D) perpendicularly onto the plane 7x + y + 3z = 0 . The attempt at a solution is attached for question 1 (actually instructor's solution) I kind of understand it but ... why is n <dot> v = equation of the plane? Does v represent all of the possible points of R^3 (certainly does not seem so...) which is projected to the normal? I understand the v-projection is there to get the projection of v onto the plane because we cannot directly project to the plane right? But why do we want v' what does v' represent and how is that the solution?