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MHT CET20244 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

The co-ordinates of the point where the line through A (3,4,1) and B (5,1,6) crosses the x y -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

Let A (x₁, y₁, z ₁ )= A (3,4,1) B (x₂, y₂, z₂ )= B (5,1,6) The equation of line passing through the points (x₁, y₁, z₁ ) and (x₂, y₂, z₂ ) is given by array ll & x-x₁ x₂-x₁ = y-y₁ y₂-y₁ = z-z₁ z₂-z₁ & x-3 5-3 = y-4 1-4 = z-1 6-1 & x-3 2 = y-4 -3 = z-1 5 array Since the line crosses the XY plane, z =0 x-3 2 = y-4 -3 = -1 5 x-3 2 = -1 5 and y-4 -3 = -1 5 x= 13 5 and y= 23 5 Required point is ( 13 5 , 23 5 , 0 )

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