If m → ,    n → are non-parallel unit vectors and r → is a vector which is perpendicular to m → and n → such that r → = 5 and m → + n → 2 = 2 + 4 m → × n → , then the value of m →    n →    r → 2 is equal to

Step-by-step solution

r → is parallel to m →   ×   n → Let θ be angle between m → and n → ∴   m → + n → 2 = 2 + 4   m → × n →   1 + 1 + 2 cos ⁡ θ = 2 + 4 × sin ⁡ θ ⇒ tan ⁡ θ = 1 2 m →   n →   r → 2 = r → . m → × n → 2 =   r → 2 m → 2 n → 2 s i n 2 θ = 25 × 1 5 = 5