Let a → = x 2 i ^ - 3 j ^ + x + 3 k ^ and b → = i ^ + 3 j ^ - x - 3 k ^ be two vectors such that a → = b → . If angle between 4 a → + 7 b → and 7 a → - 4 b → is equal to θ , then cos ⁡ 2 θ is equal to

Question

Let a → = x 2 i ^ - 3 j ^ + x + 3 k ^ and b → = i ^ + 3 j ^ - x - 3 k ^ be two vectors such that a → = b → . If angle between 4 a → + 7 b → and 7 a → - 4 b → is equal to θ , then cos ⁡ 2 θ is equal to, - 1 2, 3 2, - 1, 1 5

MARKS App · Accepted Answer

∵ a → · b → = x 2 - 9 - x 2 - 9 = 0 ⇒ a → ⊥ b → 4 a → + 7 b → ⋅ 7 a → − 4 b → = 28 a → 2 − 28 b → 2 + 33 a → ⋅ b → = 0 as a → = b → ⇒ θ = 90 o ⇒ cos ⁡ 2 θ = - 1

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