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JEE Main202524 Jan 2025Morning ShiftMathematicsThree Dimensional GeometryActual

Let in a A B C , the length of the side A C be 6 , the vertex B be (1,2,3) and the vertices A, C lie on the line x-6 3 = y-7 2 = z-7 -2 . Then the area (in sq. units) of ABC is:

Options

  1. A17
  2. B21
  3. C56
  4. D42

Correct answer

B. 21

Step-by-step solution

aligned & Let M (3 +6,2 +7,-2 +7) & BM =(3 +5) i +(2 +5) j +(-2 +4) k & AC BM =0=3(3 +5)+2(2 +5)-2(-2 +4) & BM =2 i +3 j +6 k & BM =7 & Area = 1 2 6 7=21 aligned

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