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COMEDK2017MathematicsVector Algebra

The value of [a-b b-c c-a] , where |a|=1 , | b |=5| c |=3 , is

Options

  1. A0
  2. B1
  3. C6
  4. DNone of these

Correct answer

A. 0

Step-by-step solution

[ a - b b - c c - a ]=( a - b ) [( b - c ) ( c - a )]=( a - b ) [ b c - b a - c c + c a )]=( a - b ) .[ b c - b a + c a ]= a ( b c )- a ( b a )+ a ( c a )- b ( b c )+ b ( b a )- b ( c a )=[ a b c ]-[ a b a ]+[ a c a ]-[ b b c ]+[ b b a ]-[ bca ]=[ a b c ]-[ b c a ]=0 [ a b c ]=[ b c a ]=[ c a b ]

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