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MHT CET202310 May 2023Evening ShiftMathematicsThree Dimensional GeometryActual

The plane through the intersection of planes x+y+z=1 and 2 x+3 y-z+4=0 and parallel to Y-axis also passes through the point

Options

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

Correct answer

C. (3,2,1)

Step-by-step solution

Equation of plane through the intersection of given planes is aligned & (x+y+z-1)+ (2 x+3 y-z+4)=0 (i) & (1+2 ) x+(1+3 ) y+(1- ) z+4 -1=0 aligned Since the plane is parallel to Y -axis. aligned & 1+3 =0 & = -1 3 aligned Substituting = -1 3 in (i), we get aligned & (x+y+z-1)- 1 3 (2 x+3 y-z+4)=0 & x+4 z-7=0 aligned Point (3,2,1) satisfies this equation.

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