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JEE Main202229 Jun 2022Evening ShiftMathematicsVector AlgebraActual

Let a → = i ^ - 2 j ^ + 3 k ^ , b → = i ^ + j ^ + k ^ and c → be a vector such that a → × ( b → + c → ) = 0 → , then the value of 3 c → . a → is equal to _______.

Correct answer

0

Step-by-step solution

Given, a → = i ^ - 2 j ^ + 3 k ^ ,   b → = i ^ + j ^ + k ^ And a → × ( b → + c → ) = 0 → , Let c → = x i ^ + y j ^ + z k ^ So, a → × b → + c → = 0 → ⇒ a → × b → + a → × c → = 0 → ⇒ a → × b → = - a → × c → ⇒ a → × b → = c → × a → ⇒ i ^ j ^ k ^ 1 - 2 3 1 1 1 = i ^ j ^ k ^ x y z 1 - 2 3 ⇒ - 5 i ^ + 2 j

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