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AP EAMCET2007MathematicsVector Algebra

The volume (in cubic units) of the tetrahedron with edges i + j + k , i - j + k and i +2 j - k is

Options

  1. A4
  2. B2 / 3
  3. C1 / 6
  4. D1 / 3

Correct answer

B. 2 / 3

Step-by-step solution

We know that, volume of tetrahedron aligned & = 1 6 [ A B A C A D ] & = 1 6 | array ccc 1 & 1 & 1 1 & -1 & 1 1 & 2 & -1 array | aligned aligned & = 1 6 [1(1-2)-1(-1-1)+1(2+1)] & = 1 6 [-1+2+3] & = 4 6 = 2 3 aligned

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