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AP EAMCET202422 May 2024Evening ShiftMathematicsVector AlgebraActual

If i - j - k , i + j + k , i + j +2 k and 2 i + j are the vertices of a tetrahedron then its volume is

Options

  1. A1 6
  2. B2 3
  3. C3
  4. D1 3

Correct answer

D. 1 3

Step-by-step solution

Given vertices are P = i - j - k , Q = i + j + k aligned & R = i + j +2 k , ~S =2 i + j , PQ =2 i +2 k , PR =2 j +3 k , & PS = i +2 j + k aligned aligned & Volume of tethratedron = 1 6 [ PQ PR PS ] & = 1 6 | array lll 0 & 2 & 2 0 & 2 & 3 1 & 2 & 1 array |= 1 6 [6-4]= 1 3 aligned

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