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JEE MainMathematicsVector Algebra

Let a = i - 2 j + 3 k and b = 2 i + j - k . If c is a vector satisfying the equation ( a b ) c + b ( a c ) = 0 and c ( a + 2 b ) = 45 , then the value of | c |^2 is equal to _______

Correct answer

150

Step-by-step solution

We are given the equation: ( a b ) c + b ( a c ) = 0 Expanding the first Vector Triple Product: ( a b ) c = - c ( a b ) = -[( c b ) a - ( c a ) b ] = ( a c ) b - ( b c ) a Expanding the second Vector Triple Product: b ( a c ) = ( b c ) a - ( b a ) c Substituting these expansions back into the given equation: [( a c ) b - ( b c ) a ] + [( b c ) a - ( a b ) c ] = 0 The terms involving a cancel out, leaving: ( a c ) b - ( a b ) c = 0 ( a b ) c = ( a c ) b This shows that c is a scalar multiple of b . Let c = b . Now,

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