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BITSAT2015MathematicsVector AlgebraActual

Let a, b and c be three vectors satisfying a b=(a c),|a|=|c|=1,|b|=4 and |b c|= 15 . If b-2 c = a , then equals

Options

  1. A1
  2. B-1
  3. C2
  4. D-4

Correct answer

D. -4

Step-by-step solution

Let be the angle between b and c . Given, | b c |= 15 array l | b | c | = 15 = 15 | ~b | c = 15 4 1 = 15 4 = 1- 15 16 = 1 16 = 1 4 array Now given, b -2 c = a | b -2 c ² |= a ² | b |²+4| c |-4( ~b c )= ²| a |² array l 16+4-4| ~b | c | = ² 20-16 = ² 20-4= ² ²=16 ( = 1 4 ) = 4 array

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