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MHT CET202313 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

A line drawn from the point A (1,3,2) parallel to the line x 2 = y 4 = z 1 , intersects the plane 3 x+y+2 z=5 in point B , then co-ordinates of point B are

Options

  1. A( 1 6 , 4 3 , 19 12 )
  2. B(- 1 6 ,- 4 3 , 19 12 )
  3. C( 1 6 , 4 3 ,- 19 12 )
  4. D(- 1 6 ,- 4 3 ,- 19 12 )

Correct answer

A. ( 1 6 , 4 3 , 19 12 )

Step-by-step solution

The d.r.s. of the line x 2 = y 4 = z 1 are 2,4,1 . The d.r.s. of any line parallel to it are also 2,4,1 . The equation of the line passing through A (1,3,2) is x-1 2 = y-3 4 = z-2 1 = (say) Then, any point on the line is B =(2 +1,4 +3, +2) The point B lies on the plane 3 x+y+2 z=5 . array ll & 3(2 +1)+4 +3+2( +2)=5 & 12 +10=5 & = -5 12 & B= ( 1 6 , 4 3 , 19 12 ) array

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