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KCET2013MathematicsVector Algebra

If a , b and c are unit vectors such that a + b + c =0 , then a b + b c + c a is equal to

Options

  1. A3 2
  2. B- 3 2
  3. C2 3
  4. D1 2

Correct answer

B. - 3 2

Step-by-step solution

Given that, a, b and c are unit vectors. i.e., |a|=|b|=|c|=1...(i) Now, we have gathered (a+b+c)=0 |a+b+c|²=|0|² |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 [from Eq. (i)] (a b+b c+c a)=- 3 2 gathered

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