The volume of the tetrahedron with vertices at (1,2,3), (4,3,2), (5,2,7), (6,4,8) is Options: A . &nbsp 22 3 B . &nbsp 11 3 C . &nbsp 1 3 D . &nbsp 16 3

Answer: Option D : D [ − − → A B − − → A C − − → A D ] = ∣ ∣ ∣ ∣ 3 1 − 1 4 0 4 5 2 5 ∣ ∣ ∣ ∣ = 3 ( 0 − 8 ) − 1 ( 20 − 20 ) − 1 ( 8 − 0 ) = − 24 − 0 − 8 = − 32 Volume of the tetrahedron = 1 6 ( 32 ) = 16 3 cubic unit.

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

Discussion Forum : Vector Algebra

Question -

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

Options:

A .

\frac{22}{3}

B .

\frac{11}{3}

C .

\frac{1}{3}

D .

\frac{16}{3}

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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