The volume of the tetrahedron with vertices at (1,2,3), (4,3,2), (5,2,7), (6,4,8

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Question

The volume of the tetrahedron with vertices at (1,2,3), (4,3,2), (5,2,7), (6,4,8) is

Options:

A . 223

B . 113

C . 13

D . 163

Answer: Option D
:
D

[- - \to A B - - \to A C - - \to A D] = ∣ ∣∣ ∣ \begin{matrix} 3 & 1 & - 1 4 & 0 & 4 5 & 2 & 5 \end{matrix} ∣ ∣∣ ∣ = 3 (0 - 8) - 1 (20 - 20) - 1 (8 - 0) = - 24 - 0 - 8 = - 32

Volume of the tetrahedron =

\frac{1}{6} (32) = \frac{16}{3}

cubic unit.

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