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JEE Main20246 Apr 2024Evening ShiftMathematicsThree Dimensional GeometryActual

Let P ( , , ) be the image of the point Q (3,-3,1) in the line x-0 1 = y-3 1 = z-1 -1 and R be the point (2,5,-1) . If the area of the triangle P Q R is and ^2=14 K , then K is equal to :

Options

  1. A36
  2. B81
  3. C72
  4. D18

Correct answer

B. 81

Step-by-step solution

aligned & RQ = 1+64+4 = 69 & RQ = -8 j +2 k & RS = + j - k & = RQ RS | RQ || RS | = | 1-8-2 69 3 |= 9 3 23 & = 3 23 = RS RQ = RS 69 & RS =3 3 & = 14 23 = QS 69 aligned aligned & QS = 42 & area = 1 2 2 QS RS = 42 3 3 & =9 14 & ^2=81.14=14 k & k =81 aligned

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