A vector A → is rotated by a small angle ∆ θ radians ∆ θ ≪ 1 to get a new vector B → . In that case B → - A → is :

Step-by-step solution

B → = A → B → - A → = A → 2 + A → 2 + 2 A → A → cos 180 ° - ∆ θ = A → 2 + A → 2 - 2 A → 2 cos ∆ θ = 2 A → 2 - 2 A → 2 cos ∆ θ = 2 A → 2 1 - cos ∆ θ ∵ 1 - cos ∆ θ = 2 sin 2 ∆ θ 2 = 2 A → 2 × 2 sin 2 ∆ θ 2 = 2 A → sin ∆ θ 2 For small ∆ θ ,   sin ∆ θ 2 ≃ ∆ θ 2 B → - A &#85