**Find a basis of Rn such that the matrix B of the given linear transformation T is diagonal.**

Orthogonal Projection T onto the line in R^3 spanned by

(1 1 1)

Orthogonal Projection T onto the line in R^3 spanned by

(1 1 1)

I'm assuming (though I tend to be wrong) that I need to find a vector that is parallel to the line and 2 that are perpendicular to it and linearly independent.

So would the B matrix look something like this

1 -2 1

1 1 0

1 1 -1

?

Or am I once again way off track :)