(Solved): 3 : Let \( \mathbf{u}, \mathbf{v} \) be two non-zero vectors. Without using components prove the f ...

3 : Let \( \mathbf{u}, \mathbf{v} \) be two non-zero vectors. Without using components prove the following. a) If \( \|\mathbf{u}\|=\|\mathbf{v}\| \), show that \( (\mathbf{u}+\mathbf{v}) \) and \( (\mathbf{u}-\mathbf{v}) \) are orthogonal. b) Show that \( |\mathbf{u} \circ \mathbf{v}| \leq\|\mathbf{u}\| \cdot\|\mathbf{v}\| \). For this part we do not require the equality of norms.