1. The problem statement, all variables and given/known data This is a problem from a textbook, Riley Hobson and Bence 'Mathematical Methods for Physics and Engineering'. It asks to check the validity of a vector identity. If a, b and c are general vectors satisfying a x c = b x c, does this imply c . a - c . b = c|a-b| 2. The attempt at a solution According to the book the identity is satisfied, but I think that there should be a plus/minus sign before the RHS, since we don't know whether the vectors a-b and c are in the same or opposite directions.