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AP EAMCET2009MathematicsVector Algebra

The volume of the tetrahedron having the edges i +2 j - k , i + j + k , i - j + k as coterminous, is 2 3 cubic unit. Then equals

Options

  1. A1
  2. B2
  3. C3
  4. D4

Correct answer

A. 1

Step-by-step solution

aligned & Let a = i +2 j - k , b = i + j + k & and c = i - j + k aligned Since, volume of tetrahedron = 1 6 [ a b c ] array ll & 2 3 = 1 6 | array rrr 1 & 2 & -1 1 & 1 & 1 1 & -1 & array | & 2 3 = 1 6 [1( +1)-2( -1)-1(-1-1)] & 4=[- +5] =1 array

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