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WBJEE2020MathematicsThree 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+14 y+13 z+37=0
  2. B8 x-14 y-13 z-37=0
  3. C8 x-14 y-13 z+37=0
  4. DNone of the above

Correct answer

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

Step-by-step solution

The equation of plane passing through ((2,-1,-3) ) is (a(x-2)+b(y+1)+c(z+3)=0 ) Also, as the plane is parallel is the given two lines, ( 3 a+2 b-4 c=0 ) and (2 a-3 b+2 c=0 ) ( a =-8, ~b =-14, c =-13 ) ( ) The equation of the required plane is (-8(x-2)-14(y+1)-13(z+3)=0 ) ( 8 x+14 y+13 z+37=0 ) So the answer is (a).

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