find the matrix for ProjL with respect to the basis

Let L be the line in R3 spanned by v1=[1 1 1]

(a)Find a basis {v1, v2} for the plane perpendicular to L.

(b) Let ProjL be the projection onto the line L. Find the matrix for ProjL with respect to the basis B.

Sol: We need to find 2 vectors that span the above plane, that is, we need to find the null space of the matrix. I got [1 1 1 0], which is already in row reduced echelon form. After doing some algebra, I got span([0 -1 1], [-1 0 1]). Therefore, the basis of R3 is {[0 -1 1], [-1 0 1]} right? But I don't get part (b). Help!