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JEE Main20245 Apr 2024Morning ShiftMathematicsStraight LinesActual

If A (1,-1,2), B (5,7,-6), C (3,4,-10) and D (-1,-4,-2) are the vertices of a quadrilateral A B C D , then its area is :

Options

  1. A48 7
  2. B12 29
  3. C24 7
  4. D24 29

Correct answer

B. 12 29

Step-by-step solution

aligned & A (1,-1,2) & B (5,7,-6) & C (3,4,-10) & D (-1,-4,-2) & Area = 1 2 | AC BD |= 1 2 |(2 i +5 j -12 k ) (6 i +11 j -4 k )| & = 1 2 |112 i -64 j -8 k | & =4|14 i -8 j - k | & =4 196+64+1 & =4 261 & =12 29 aligned

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