In a vector space, given 3 vectors I want to find all solutions of .

So far this is my approach, I am just a little hestiant to say I have found all solutions:

If we assume and . Then because we know equality of Cauchy- Schwarz holds iff one vector is a scalar multiple of the other.

So

Using this fact I know is a solution.

The cases when a,b or c is 0 are less interesting I think. What do you think?