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MHT CET202015 Oct 2020Evening ShiftMathematicsVector AlgebraActual

The volume of a tetrahedron whose vertices are A (-1,2,3), B (3,-2,1) , C (2,1,3) and D (-1,-2,4) is

Options

  1. A14 3 cu. units
  2. B16 3 cu. units
  3. C17 3 cu. units
  4. D15 3 cu. units

Correct answer

B. 16 3 cu. units

Step-by-step solution

Here AB =4 i -4 j -2 k , AC =3 i - j and AD =-4 j + k Volume of tetrahedron array l = 1 6 AB ( AC AD ) = 1 6 | array ccc 4 & -4 & -2 3 & -1 & 0 0 & -4 & 1 array |= 1 6 [4(-1)+4(3)-2(-12)] = 1 6 (32)= 16 3 cu.units array

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