1.Points aren't orthogonal to anything. Vectors or lines can be orthogonal. This statement is a category error.And I know that those points are orthogonal to each other.
2. Since the RBYV system appears to be attached to your object, where is your origin? Is it V? If not, I don't see how you can compute the location of V using only the coordinates of R, B, and Y. You would have to know lengths from those points to V, and even then you'd have two solutions, probably. At least, as an example, if V is equidistant from R, B, and Y, then there are two possible locations for V, one on either side of the plane containing R, B, and Y. Is there a handed-ness that you can invoke? Such as VY x VR = VB? (That's a vector cross product there). That could eliminate one of your two solutions, I think.
3. Use rotation matrices to represent rotations of a vector about a particular axis.
Hope this helps.