Let T : R^3 -> R^3 be orthogonal projection onto the plane x + y + z = 0.

a) Show that the closest point to (1,0,0) on the plane x + y + z = - is (2/3,-1/3,-1/3).

b) Show that the standard matrix for T is A = 1/3[2 -1 -1; -1 2 -1; -1 -1 2]

Can anyone show me how to do (a)? I'm not sure I have done it right. I first found the basis for the plane: {(-1,1,0),(-1,0,1)} (correct?) and then changed it to an orthonormal basis. Then I went on to find the orthogonal projection of (1,0,0) using the orthonormal basis vectors.

Any ideas about (b)?