- Prove that if and , then at least one of is the zero vector. Give a geometric interpretation of this result.
- Prove that if is a nonzero vector, and if and then .
- Proof. If we have then
But, since we know and are orthogonal, so . Therefore, we must have either or . Hence, either or is the zero vector
- Proof. First,
But, and implies or (by part (a)). Since by hypothesis, we must have . Hence,