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


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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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