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AP EAMCET201824 Apr 2018Morning ShiftMathematicsVector AlgebraActual

a, b and c are three unit vectors such that no two of them are collinear. If b =2 a ( b c ) and is the angle between a , c and is the angle between a , b , then ( + )=

Options

  1. A3 2
  2. B- 3 2
  3. C1 2
  4. D- 1 2

Correct answer

B. - 3 2

Step-by-step solution

We have, aligned & b =2 a ( b c ) & b =2 ( a c ) b -( a b ) c & b =2( a c ) b -2( a b ) c aligned On comparing b and c , we get 2( a c )=1 and a b =0 is a angle between a , c and is the angle between a , b . aligned | a || c | & = 1 2 , a b =0 & = 3 , and = 2 & = / 3 and = 2 ( + ) & =- / 3=- 3 / 2 aligned

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