Let a → ,   b → and c → be three unit vectors, out of which vectors b → and c → are non-parallel. If α and β are the angles which vector a → makes with vectors b → and c → respectively and a → × b → × c → = 1 2 b → , then α - β is equal to :

Step-by-step solution

a → × b → × c → = b → 2 ⇒ a → . c → b → - a → . b → c → = b → 2 Since, b → is not parallel to c → ⇒ a → . c → = 1 2 ⇒ a c cos β = 1 2 ⇒ cos β = 1 2 and a → . b → = 0 ⇒ a b cos α = 0 ⇒ cos α = 0 ⇒ β = π 3 and α = π 2 ∴ α - β = π 2 - π 3 = π 6