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KCET2017MathematicsFunctions

If ( a , b , c ) are unit vectors such that ( a + b + c = 0 ) then the value of ( a b + b c + c a ) is equal to

Options

  1. A( 1 )
  2. B( 3 )
  3. C( - 3 2 )
  4. D( 3 2 )

Correct answer

C. ( - 3 2 )

Step-by-step solution

For unit vectors, we know that [ | a |=| b |=| c |=1 (1) ] [ Given that, a + b + c = 0 ] Squaring on both sides of Eq. (1), [ array l | a |²+| b |²+| c |²+2( a b + b c + c a )=0 1+1+1+2( a b + b c + c a )=0 a b + b c + c a = -3 2 array ]

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