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COMEDK2018MathematicsVector Algebra

The volume of the tetrahedron formed by the points (1,1,1),(2,1,3)(3,2,2) and (3,3,4) in cubic units is

Options

  1. A5 6
  2. B6 5
  3. C5
  4. D2 3

Correct answer

A. 5 6

Step-by-step solution

Let A(1,1,1), B(2,1,3), C(3,2,2) and D(3,3,4) . So, A B = i +2 k , A C =2 i + j + k and A D =2 i +2 j +3 k aligned & Volume of tetrahedron = 1 6 [ array lll 1 & 0 & 2 2 & 1 & 1 2 & 2 & 3 array ] & = 1 6 |1(3-2)+0(6-2)+2(4-2)| &= 1 6 (1+0+4)= 5 6 cubic units aligned

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