u= (((3i + j) dotted with (i + j)) * (i +j)) / (|i = j|^2). I tried to simplify to

u = (3i + j)*(i + j) / (i^2 +j^2) and from here i don't know how to simplify further. Apparently it is simplified to 4/2 (i + j) = 2i + 2j.

The initial question states, express the vector 3i + j as a su of vectors u + v, where u is parallel to vector i + j and v is perpendicular to u. I am interested in the vector projection solution.

Help would be nice!