Linear Algebra: orthogonal components of a vector

1. The problem statement, all variables and given/known data
Let V = Gen{ [0;5;1;2], [4;0;-2;1], [5,1,0,1]}. Define u1₁=v₁. Indicate the coordinates of u₂, the orthogonal component of v₂ to V₁=Gen{u₁.


2. Relevant equations
I know V has to be a vector space. If there is a subspace W with an orthogonal basis B={v₁,...,v_k} then the orthogonal component of any vector u to W is

u_c=u - (<u,v₁>/<v₁,v₁>)*v₁ - ... - (<u,v_k>/<v_k,v_k>)*v_k


3. The attempt at a solution
I don-t even know where to start since the basis given is not orthogonal. Do I have to construct an orthogonal basis from the three vectors given and then proceed to solve it? I didn't see this topic in class so I didn't see the professor do this, I'm doing this for extra credit on the subject. Anyone knows where I could find a worked out example of this type of problems? Thank you.