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JEE Main202116 Mar 2021Evening ShiftMathematicsVector AlgebraActual

Let c → be a vector perpendicular to the vectors a → = i ^ + j ^ - k ^ and b → = i ^ + 2 j ^ + k ^ . If c → · ( i ^ + j ^ + 3 k ^ ) = 8 , then the value of c → · ( a → × b → ) is equal to

Correct answer

0

Step-by-step solution

c → = λ ( a → × b → ) a → × b → = i ^ j ^ k ^ 1 1 - 1 1 2 1 ( a → × b → ) = 3 i ^ - 2 j ^ + k ^ c → · ( i ^ + j ^ + 3 k ^ ) = λ ( 3 i ^ - 2 j ^ + k ^ ) · ( i ^ + j ^ + 3 k ^ ) ⇒ λ ( 4 ) = 8 ⇒ λ = 2 c → = 2 ( a → × b → ) Hence, c → · ( a → × b → ) = 28

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