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MHT CET202526 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual

The equation of the plane passing through the point (1,1,1) and through the line of intersection of x+2 y-z+1=0 and 3 x-y-4 z+3=0 is

Options

  1. A4 x-3 y-2 z+1=0
  2. B3 x-2 y+2 z-3=0
  3. C8 x-5 y-11 z+8=0
  4. D5 x-4 y+2 z-3=0

Correct answer

C. 8 x-5 y-11 z+8=0

Step-by-step solution

Plane through intersection and point For planes P₁: x+2y-z+1=0 and P₂: 3x-y-4z+3=0 , the family of planes through their line of intersection is given by P₁ + P₂ = 0 : (x+2y-z+1) + (3x-y-4z+3) = 0 Substituting point (1,1,1) determines : 3 + (1) = 0 = -3 x+2y-z+1 - 3(3x-y-4z+3) = 0 -8x + 5y + 11z - 8 = 0 Multiplying by -1 yields 8x - 5y - 11z + 8 = 0 , which corresponds to option C. Final answer: C

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