To find the projection of $v = [14 ,11,-9 ]^t $ onto the subspace spanned by $u_1 = [1 ,4,-1]^t$ and $u_2 = [6 ,0,-4]^t$.

Question

To find the projection of $v = [14 ,11,-9 ]^t $ onto the subspace spanned by $u_1 = [1 ,4,-1]^t$ and $u_2 = [6 ,0,-4]^t$.

Let $V$ be the subspace spanned by $u_1,u_2$ .

$proj_V(v) = proj_{u_1}(v) + proj_{u_2}(v) = \frac{<v,u_1>}{<u_1,u_1>}u_1 + \frac{<v,u_2>}{<u_2,u_2>}u_2 = \frac{67}{18}u_1 + \frac{30}{13}u_2.$

Is the solution correct?