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AP EAMCET201923 Apr 2019Morning ShiftMathematicsVector AlgebraActual

If ( a , b , c ) are three unit vectors such that ( a ( b c )= 3 2 b + 1 2 c ), then the angles between ( a , b ) and ( a , c ) respectively are

Options

  1. A(60^ , 30^ )
  2. B(120^ , 30^ )
  3. C(60^ , 150^ )
  4. D(120^ , 150^ )

Correct answer

B. (120^ , 30^ )

Step-by-step solution

Given that ( a ( b c )= 3 2 b + 1 2 c ) ( (a . c) b - ( a b ) c = 3 2 b + 1 2 c ) Let angle between unit vectors ( a ) and ( c ) is ' ( ) ' and angle between unit vectors ( a ) and ( b ) is ' ( ) ', then ( array rlrl & ( ) b -( ) c = 3 2 b + 1 2 c & = 3 2 and =- 1 2 & & =30^ and =120^ array ) Hence, option (b) is correct.

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