Answer:
[tex]\mathbf{V = \dfrac{16}{3}}[/tex]
Step-by-step explanation:
From the information given:
A = (4,0,0) B = (0,4,0) C = (0,0,1) D = (4,4,1)
[tex]\overline{ AB}[/tex] = (0,4,0) - (4,0,0) = (-4, 4, 0)
[tex]\overline{ BC} =[/tex] (0,0,1) - (0,4,0) = (0, -4, 1)
[tex]\overline{ CD}[/tex] = (4,4,1) - (0,0,1) = (4, 4, 0)
The Volume of the tetrahedron [tex]V = \dfrac{1}{6} \bigg| AB \times BC \times CD \bigg|[/tex]
The Volume of the tetrahedron [tex]V = \dfrac{1}{6} \left\begin{vmatrix}-4,&4&0\\0,&-4&1\\4&4&0\end{vmatrix}\right[/tex]
[tex]V = \dfrac{1}{6}\bigg [ -4(-4 *0 - 1*4) -4(0*0-1*4) +0(0*4--4*4) \bigg ][/tex]
[tex]V = \dfrac{1}{6}\bigg [ -4(0 - 4) -4(0-4) +0(0+16) \bigg ][/tex]
[tex]V = \dfrac{1}{6}\bigg [ 16 + 16 +0 \bigg ][/tex]
[tex]V = \dfrac{1}{6}\bigg [ 32 \bigg ][/tex]
[tex]\mathbf{V = \dfrac{16}{3}}[/tex]
