What is the angle between vector A and vector B for which modA plus B is equal to modA-B?

Answer 1

The condition ( | \mathbf{A} + \mathbf{B} | = | \mathbf{A} - \mathbf{B} | ) implies that the vectors are oriented such that their magnitudes are equal when added and subtracted. This occurs when the angle ( \theta ) between vectors ( \mathbf{A} ) and ( \mathbf{B} ) is ( 90^\circ ) (or ( \frac{\pi}{2} ) radians). Thus, the angle between vector ( \mathbf{A} ) and vector ( \mathbf{B} ) is ( 90^\circ ).