MHT CET202014 Oct 2020Evening ShiftMathematicsVector AlgebraActual

If [ a b c ]=3 , then the volume of the parallelopiped with 2 a + b , 2 b + c , 2 c + a as coterminus edges is

Options

A22 cubic units
B15 cubic units
C27 cubic units
D25 cubic units

Correct answer

C. 27 cubic units

Step-by-step solution

Volume of parallelepiped array l =(2 a + b ) [(2 b + c ) (2 c + a )] =(2 a + b ) [(4 b c )+(2 b a )+(2 c c )+( c a )] =[8 a ( b c )]+[4 a ( b a )]+[2 a ( c a )]+[4 b ( b c )]+[2 b ( b a )]+[ b ( c a )] =[8 a ( b c )]+0+[ b ( c a )] =8[ a ( b c )]+[ a ( b c )]=9 a ( b c ) =9[ a b c ]=9(3)=27 array

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