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KCET2011MathematicsVector Algebra

If a , b and c are non-coplanar, then the value of a b c 3 b ( c a ) - b c a 2 c ( a b ) is

Options

  1. A- 1 2
  2. B- 1 3
  3. C- 1 6
  4. D1 6

Correct answer

C. - 1 6

Step-by-step solution

Given, [a b c] 0 , i.e., non-coplanar. aligned &= a a c 3 b ( c a ) - b c a 2 c ( a c ) &= a ( b c ) 3 b ( c a ) - b ( c a ) 2 c ( a b ) &= [ a b c ] 3[ b c a ] - [ b c a ] 2[ c a b ] ( a ( b b )=[ a b c ] &= [ b c a ]=[ a b c ],[ c a b ]=[ b c a ] 3[ a b ~ c ] - [ b c a ] 2[ b c a ] &=1 / 3-1 / 2=-1 / 6 aligned

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