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JEE Main202324 Jan 2023Evening ShiftMathematicsVector AlgebraActual

Let a → = i ^ + 2 j ^ + λ k ^ , b → = 3 i ^ - 5 j ^ - λ k ^ , a → · c → = 7 , 2 b → · c → + 43 = 0 , a → × c → = b → × c → , then a → · b → is equal to

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0

Step-by-step solution

Given: a → × c → = b → × c → ⇒ a → × c → - b → × c → = 0 ⇒ a → - b → × c → = 0 So, a → - b → ∥ c → , hence a → - b → = μ c → where, μ is any scalar. ⇒ - 2 i ^ + 7 j ^ + 2 λ k ^ = μ c →       . . . . 1 Taking dot product with a → , we get ⇒ - 2 + 14 + 2 λ 2 = 7 μ ⇒ 7 μ = 2 λ 2 + 12   &

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