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MHT CET202310 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

The line x-2 3 = y-1 -5 = z+2 2 lies in the plane x+3 y- z+ =0 , then the value of ^2+ + ^2 is

Options

  1. A127
  2. B43
  3. C109
  4. D61

Correct answer

B. 43

Step-by-step solution

Line x-2 3 = y-1 -5 = z+2 2 lies in the plane x+3 y- z+ =0 The direction ratios of the line are 3,-5,2 . The direction ratios of the normal to the plane are 1,3,- . The given line is perpendicular to the normal of plane. aligned & 3(1)+(-5)(3)+2(- )=0 & 3-15-2 =0 & -12-2 =0 & =-6 aligned Also, point (2,1,-2) lies on the plane aligned & x+3 y- z+ =0 & 2+3-(-6)(-2)+ =0 & 2+3-12+ =0 & =7 & ^2+ + ^2=36-42+49=43 aligned

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