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MHT CET20243 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

On which of the following lines lies the point of intersection of the line, x-4 2 = y-5 2 = z-3 1 and the plane x+y+z=2 ?

Options

  1. Ax-1 1 = y-3 2 = z+4 -5
  2. Bx-4 1 = y-5 1 = z-5 -1
  3. Cx-2 2 = y-3 2 = z+3 3
  4. Dx+3 3 = 4-y 3 = z+1 -2

Correct answer

A. x-1 1 = y-3 2 = z+4 -5

Step-by-step solution

Let x-4 2 = y-5 2 = z-3 1 = x=2 +4, y=2 +5, z= +3 Given line lies on plane x+y+z=2 aligned & (2 +4,2 +5, +3) lies on & x+y+ z =2 & (2 +4+2 +5+ +3)=2 & 5 +12=2 & =-2 aligned (0,1,1) lies on required plane. (0,1,1) satisfies option (A) i.e., x-1 1 = y-3 2 = z+4 -5

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