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MHT CET2012MathematicsVector Algebra

If the position vectors of the vertices A, B and C are 6i, 6 j and k respectively w.r.t. origin O , then the volume of the tetrahedron O A B C is

Options

  1. A6
  2. B3
  3. C1 6
  4. D1 3

Correct answer

A. 6

Step-by-step solution

Given that, the position vectors of the vertices A, B and C are array l O A =6 i =6 i +0 j +0 k O B =6 j =0 i +6 j +0 k O C = k =0 i +0 j + k array Now, volume of the tetrahedron array l = 1 6 [ O A O B O C ] = 1 6 | array lll 6 & 0 & 0 0 & 6 & 0 0 & 0 & 1 array | = 1 6 (6 6 1)=6 array

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