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KCET2017MathematicsThree Dimensional Geometry

If ( a & b ) are unit vectors, then the angle between ( a ) and ( b ) for ( 3 a - b ) to be unit vector is

Options

  1. A( 30^ )
  2. B( 45^ )
  3. C( 60^ )
  4. D( 90^ )

Correct answer

A. ( 30^ )

Step-by-step solution

Since a and b are unit vectors. Then, | a |=| b |=1 also, | 3 a - b |=1 (1) which is also unit vector. Squaring both the sides of Eq. (1), we get 3| a |²+| b | r -2 3 | a | | b |=(1)²3 1+1-2 3 1 1 =1 2 3 =3 = 3 2 3 = 3 2 =30^

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