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

Question

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, 7, 21 5, 5, 10 3

MARKS App · Accepted Answer

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

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