Let L be the line spanned by v_1=[1, 1, 1]. Find a basis {v_2, v_3} for the plane perpendicular to L, and verify that B= {v_1,, v_2, v_3} is a basis for R3.

Let ProjL denote the projection onto the line L. Find the matrix B for ProjL with respect to the basis B.

Can you just help me get started with the problem. I'll do the rest on my own.