I am having difficulty solving a problem presented to me by a fellow classmate. I was given a diagram, but I will describe the problem without one, as it is not necessary to fully understand the problem:
Let v and u be an arbitrary vectors in 3 dimensions. If the angle between v and u is $\lambda$ and u makes an angle $\theta$ with the positive x axis ($cos\alpha=\theta$ for u), show that the direction cosines for v can be expressed as
where $cos\alpha$, $cos\beta$, and $cos\gamma$ are the angles v makes with the positive x, y, and z axes respectively.
I approached this problem using the formula for the angle between to vectors, since it gives a easily manageable expression for $cos\lambda$, but I keep arriving at fallacious statements. Any help would be appreciated. Thank you.