If [ ( a+2 b+3 c ) ( b+2 c+3 a ) ] ( c+2 a+3 b )=54, then the value of [ a b c] is

MHT CET 2023 Mathematics question

If , then the value of is

(A)0
(B)1
(C)3Correct
(D)2

Answer: (C)

Solution

The expression is the scalar triple product of three vectors whose coefficients with respect to form the rows , , . For linear combinations, \vec\vec\vec\det$(\text{coefficient

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Question ID VK-094801