1. The problem statement, all variables and given/known data (a)2 + a · b - c = 0 a and b are vectors which (in general) with different directions while c is a scalar. How to solve for a?3. The attempt at a solution (a)2 + a · b - c = 0 (a + (1/2)b)2 - (1/4)b2 - c = 0 (a + (1/2)b)2 = (1/4)b2 + c In this case, if i carry the square from left hand side to right hand side, it appears that the left hand side turns into a vector while the right hand side remains as a scalar. I wonder why this happens and what would be the proper way to solve this equation.