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MHT CET202521 Apr 2025Morning ShiftMathematicsVector AlgebraActual

Let a , ~b , and c be unit vectors. Suppose that a ~b = a c =0 and if the angle between b and c is 6 , then a is

Options

  1. A( b c )
  2. B1 2 ( ~b c )
  3. C2( ~b c )
  4. D4( ~b c )

Correct answer

C. 2( ~b c )

Step-by-step solution

Given that a , b , and c are unit vectors with a b = 0 and a c = 0 , a is perpendicular to both b and c . Since a is orthogonal to b and c , it must be parallel to b c , so a = k( b c ) for some scalar k . Using the unit magnitude of a , |k|| b c | = 1 . The magnitude | b c | = | b || c | = 1 1 ( 6 ) = 1 2 . Thus, |k| 1 2 = 1 , giving |k| = 2 , so k = 2 . Therefore, a = 2( b c ) , matching option C .

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