Question

8. For any vectors \( A, B \), prove the following relations: (a) \( \|A+B\|^{2}+\|A-B\|^{2}=2\|A\|^{2}+2\|B\|^{2} \). (b) \( \|A+B\|^{2}=\|A\|^{2}+\|B\|^{2}+2 A \cdot B \). (c) \( \|A+B\|^{2}-\|A-B\|