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?