Two vectors A → and B → have equal magnitudes. If magnitude of A → + B → is equal to two times the magnitude of A → - B → , then the angle between A → and B → will be

Step-by-step solution

Given: A → + B → = 2 A → - B → We have, A 2 + A 2 + 2 A 2 cos θ = 4 A 2 + A 2 - 2 A 2 cos θ Simplifying we get 2 A 2 + 2 A 2 cos θ = 8 A 2 - 8 A 2 cos θ ⇒ 1 + cos θ = 4 - 4 cos θ ⇒ 5 cos θ = 3 ⇒ cos θ = 3 5 ⇒ θ = cos - 1 3 5