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JEE Main20266 April 2026Morning ShiftMathematicsVector AlgebraActual

If a = i + j + k , b = j - k and c be three vectors such that a c = b and a c = 3 , then c ( a - 2 b ) is equal to _______.

Correct answer

0

Step-by-step solution

Given a c = b . Taking the dot product with c on both sides: ( a c ) c = b c Since the scalar triple product with two identical vectors is zero, we get: b c = 0 We need to find the value of c ( a - 2 b ) . Expanding the dot product: c ( a - 2 b ) = c a - 2( c b ) It is given that a c = 3 . Substituting the values: c ( a - 2 b ) = 3 - 2(0) = 3 Answer: 3

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