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BITSAT2017MathematicsThree Dimensional GeometryActual

The image of the point ( 1 , 6 , 3 ) in the line x 1 = y - 1 2 = z - 2 3 is

Options

  1. A( - 1 , 0 , 7 )
  2. B( - 1 , 0 , - 7 )
  3. C( 1 , 0 , 7 )
  4. D( 2 , 0 , 7 )

Correct answer

C. ( 1 , 0 , 7 )

Step-by-step solution

Let P ( 1 , 6 , 3 ) be the given point and L be the foot of perpendicular from P to the given line. The coordinates of a general point on the given line are x - 0 1 = y - 1 2 = z - 2 3 = λ (say) i.e. x = λ y = 2 λ + 1 ,   z = 3 λ + 2 If the coordinates of L are ( λ , 2 λ + 1 , 3 λ + 2 ) , then the direction ratios of P L are ( λ - 1 , 2 λ - 5 , 3 λ - 1 ) . Since, the direction ratios of given line which is perpendicular to P L , are 1 , 2 and 3 . Therefore, ( &

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