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BITSAT2013MathematicsThree Dimensional GeometryActual

The coordinates of the point where the line through the points A (3,4,1) and B (5,1,6) crosses the XY-plane are

Options

  1. A( 13 5 , 23 5 , 0 )
  2. B(- 13 5 , 23 5 , 0 )
  3. C( 13 5 ,- 23 5 , 0 )
  4. D(- 13 5 , -23 5 , 0 )

Correct answer

A. ( 13 5 , 23 5 , 0 )

Step-by-step solution

Equation of the line through the given points is x-3 5-3 = y-4 1-4 = z-1 6-1 x-3 2 = y-4 -3 = z-1 5 Any point on this line can be taken as (3+2 , 4-3 , 1+5 ) If this point lies on XY-plane then the z-coordinate is zero 1+5 =0 =- 1 5 Thus the required coordinates of the point are (3- 2 5 , 4-3 (- 1 5 ), 0 ) ( 13 5 , 23 5 , 0 )

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