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JEE Main20238 Apr 2023Morning ShiftMathematicsVector AlgebraActual

Let a → = 6 i ^ + 9 j ^ + 12 k ^ , b → = α i ^ + 11 j ^ - 2 k ^ and c → be vectors such that a → × c → = a → × b → If a → · c → = - 12 , and c → · i ^ - 2 j ^ + k ^ = 5 then c → · i ^ + j ^ + k ^ is equal to _ _ _ _ _ _ _

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Step-by-step solution

Given, a → = 6 i ^ + 9 j ^ + 12 k ^ ,   b → = α i ^ + 11 j ^ - 2 k ^ and c → be vectors such that a → × c → = a → × b → , a → × c → - a → × b → = 0 ⇒ a → × c → - b → = 0 So, a →   &   c → - b → are parallel vectors, Hence, λ a → = c → - b → ⇒ c → = b → + λ a → ⇒ a → · c → = a → &#1

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