Find-the-volume-of-tetrahedron-whose-vertices-are-the-points-A-2-1-3-B-4-1-3-C-3-2-1-and-D-1-4-2-Mastermind-

Question Number 170386 by Mastermind last updated on 22/May/22

F i n d t h e v o l u m e o f t e t r a h e d r o n w h o s e

v e r t i c e s a r e t h e p o i n t s A (2, - 1, - 3),

B (4, 1, 3), C (3, 2, - 1) a n d D (1, 4, 2) .

M a s t e r m i n d

Commented by mr W last updated on 22/May/22

a = \vec{A D} = (- 1, 5, 4)

b = \vec{B D} = (- 3, 3, - 1)

c = \vec{C D} = (- 2, 2, 3)

V = \frac{∣ a \times b \cdot c ∣}{6}

V = \frac{1}{6} | \begin{matrix} - 1 & 5 & 4 \\ - 3 & 3 & - 1 \\ - 2 & 2 & 3 \end{matrix} | = \frac{44}{6} = \frac{22}{3}

Commented by Mastermind last updated on 22/May/22

g o t s a m e

t h a n k y o u

Answered by MikeH last updated on 23/May/22

V = \frac{1}{6} | \begin{matrix} 2 & - 1 & - 3 & 1 \\ 4 & 1 & 3 & 1 \\ 3 & 2 & - 1 & 1 \\ 1 & 4 & 2 & 1 \end{matrix} | = \frac{22}{3}

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