A vector r → is equally inclined with the vectors a → = cos ⁡ θ i ^ + sin ⁡ θ j ^ ,   b → = - sin ⁡ θ i ^ + cos ⁡ θ j ^ and c → = k ^ , then the angle between r → and a → is

Step-by-step solution

a → , b → , c → are unit vectors and mutually perpendicular vectors and r → is equally inclined to all 3 vectors ⇒ r → = λ a → + b → + c → ⇒ r → = λ cos ⁡ θ - sin ⁡ θ i ^ + sin ⁡ θ + cos ⁡ θ j ^ + k ^ Angle between r → and a → is cos ⁡ α = r → ⋅ a → r → a → = λ cos 2 ⁡ θ - sin ⁡ θ cos ⁡ θ + sin 2 ⁡ θ + sin ⁡ θ cos ⁡ θ 1 × 3 λ cos ⁡ α = 1 3 ⇒ α = c o s - 1 1 3