MHT CET202014 Oct 2020Morning ShiftMathematicsVector AlgebraActual

If A (-1,2,3), B (3,-2,1), C (2,1,3) and D (-1,-2,4) are the vertices of a tetrahedron, then its volume is

Options

A16 3 Cu. units
B13 6 cu. units
C16 31 CU. units
D31 6 cu. units

Correct answer

A. 16 3 Cu. units

Step-by-step solution

We have A B =4 i -4 j -2 k , A C =3 i - j and A D =-4 j + k Volume of tetrahedron = 1 6 [ AB AC AD ] array l = 1 6 | array ccc 4 & -4 & -2 3 & -1 & 0 0 & -4 & 1 array | = 1 6 [4(-1)+4(3)-2(-12)]= 1 6 (-4+12+24)= 32 6 = 16 3 array

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