Question

71. If the magnitude of the sum of the two vectors is equal to
the difference of their magnitudes, then the angle between
vectors is
(a) 0°
(b) 45°
(c) 90°
(d) 180°​

Answer 1

Answer:

Let the vectors be A, B

let sum be, S

S² = A² + B² + 2ABcosθ

Difference be, D

D² = A² + B² - 2ABcosθ

given S = D  ⇒ S² = D²

A² + B² + 2ABcosθ  =  A² + B² - 2ABcosθ

4ABcosθ = 0 ⇒ cosθ = 0 ⇒ θ = 90° or 270°

mean A and B are perpendicular to each other