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NDA2017MathematicsThree Dimensional GeometryActual

The point of intersection of the line joining the points (-3,4,-8) and (5,-6,4) with the XY-plane is

Options

  1. A( 7 3 ,- 8 3 , 0 )
  2. B(- 7 3 ,- 8 3 , 0 )
  3. C(- 7 3 , 8 3 , 0 )
  4. D( 7 3 , 8 3 , 0 )

Correct answer

A. ( 7 3 ,- 8 3 , 0 )

Step-by-step solution

The equation of the line joining the points (-3,4,-8) and (5,-6,4) is aligned & x+3 8 = y-4 -10 = z+8 12 =k( say ) & x+3=8 k ; y-4=-10 k ; z+8=12 k & x=8 k-3 ; y=-10 k+4 ; z=12 k-8 aligned Given that this line intersects with xy plane. So , z =0 12 k -8=0 12 k =8 k = 8 12 = 2 3 . x=8 ( 2 3 )-3 ; y=-10 ( 2 3 )+4 ; z=12 ( 2 3 )-8 x = 16 3 -3 ; y = -20 3 +4 ; z = 24 3 -8 aligned & x = 7 3 ; y = -8 3 ; z =0 & ( x , y , z )= ( 7 3 , -8 3 , 0 ) aligned

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