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MHT CET202410 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

The equation of the plane through the point (2,-1,-3) and parallel to the lines x-1 3 = y+2 2 = z -4 and x 2 = y-1 -3 = z-2 2 is

Options

  1. A8 x+y-13 z+27=0
  2. B2 x+y+z=0
  3. C3 x-y-z-10=0
  4. D8 x+14 y+13 z+37=0

Correct answer

D. 8 x+14 y+13 z+37=0

Step-by-step solution

Equation of the plane passing through a and parallel to b and c is r ( b c )= a ( b c ) aligned & b c = | array ccc i & j & k 3 & 2 & -4 2 & -3 & 2 array |=-8 i -14 j -13 k & aligned & a ( b c ) & =(2)(-8)+(-1)(-14)+(-3)(-13) & =-16+14+39=37 aligned aligned Required equation is r (-8 i -14 j -13 k )=37 i.e., 8 x+14 y+13 z+37=0

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