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BITSAT2010MathematicsVector AlgebraActual

With respect to a rectangular cartesian coordinate system, three vectors are expressed as : ( a =4 i - j , b =-3 i +2 j ) and ( c =- k ) where ( i , j , k ) are unit vectors, along the (X ), (Y ) and (Z )-axis respectively. The unit vector ( r ) along the direction of sum of these vector is -

Options

  1. A( r = 1 3 ( i + j - k ) )
  2. B( r = 1 2 ( i + j - k ) )
  3. C( i = 1 3 ( i - j + k ) )
  4. D( r = 1 2 ( i + j + k ) )

Correct answer

A. ( r = 1 3 ( i + j - k ) )

Step-by-step solution

( aligned & r = a + b + c =4 i - j -3 i +2 j - k = i + j - k & r = r | r | = i + j - k 1^2+1^2+(-1)^2 = i + j - k 3 aligned )

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