Proving Orthogonal Projection of Triangle V, v'_{1}

[rannasquaer]

Given the triangle above where $$V < v'_{1}$$, prove that the \[ v_{1}=V \cos(\psi)+v'_{1} \cos(\theta - \psi) \]

It is said that $$v_{1}$$ is equal to the sum of the orthogonal projections on $$v_{1}$$ of $$V$$ and of $$v'_{1}$$ and that is precisely the expression that show. But I couldn't see how to make the projection and the calculations.

 

[Opalg]