1. The problem statement, all variables and given/known data If w is orthogonal to u and v, then show that w is also orthogonal to span ( u , v ) 2. Relevant equations two orthogonal vectors have a dot product equalling zero 3. The attempt at a solution I can see this geometrically in my mind, and I know that w . u = 0 and w . v = 0 but I don't know or understand how I can show this for its span in writing.