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JEE Main201911 Jan 2019Morning ShiftMathematicsThree Dimensional GeometryActual

The plane containing the line x-3 2 = y+2 -1 = z-1 3 and also containing its projection on the plane 2 x +3 y - z =5 , contains which one of the following points?

Options

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

Correct answer

D. (2,0,-2)

Step-by-step solution

Let normal to the required plane is n n is perpendicular to both vector 2 i - j +3 k and 2 i +3 j -3 k n = | array ccc i & j & k 2 & -1 & 3 2 & 3 & -1 array |=-8 i +8 j +8 k Equation of the required plane is (x-3)(-8)+(y+2) 8+(z-1) 8=0 (x-3)(-1)+(y+2) 1+(z-1) 1=0 x-3-y-2-z+1=0 x-y-z=4 passes through (2,0,-2) plane contains (2,0,-2)

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