If vectors 4 p → + q → , 2 p → - 3 q → and 5 p → - 3 q → , 5 p → + 3 q → are a pair of mutually perpendicular vectors and if the angle between p → and q → is θ , then the value of s i n 2 θ is equal to

Question

If vectors 4 p → + q → , 2 p → - 3 q → and 5 p → - 3 q → , 5 p → + 3 q → are a pair of mutually perpendicular vectors and if the angle between p → and q → is θ , then the value of s i n 2 θ is equal to, 3 5, 9 25, 1 2500, 2499 2500

MARKS App · Accepted Answer

4 p → + q → ⋅ 2 p → - 3 q → = 0 8 p → 2 - 3 q → 2 = 10 p → ⋅ q → … 1 5 p → - 3 q → ⋅ 5 p → + 3 q → = 0 ⇒ 25 p → 2 = 9 q → 2 … 2 cos ⁡ θ = p → ⋅ q → p → q → = 8 p → 2 - 3 q → 2 10 p → q → = 8 9 25 - 3 10 × 3 5 ⇒ cos ⁡ θ = - 3 25 6 = - 1 50 ⇒ s i n 2 θ = 2499 2500 ∵ θ ∈ 0 , π

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