Answer :
Answer:
The volume of the tetrahedron is
[tex]\frac{-32}{3}[/tex]
Step-by-step explanation:
To find the volume of a tetrahedron with vertices (2, 0, 0), (0, 4, 0), (0, 0, 4), (2, 4, 4).
We know by definition that the volume of a tetrahedron with vertices [tex](x_{1}, y_{1}, z_{1}), (x_{2}, y_{2}, z_{2}), (x_{3}, y_{3}, z_{3})[/tex] is
[tex]\frac{1}{6}\begin{vmatrix}
2 & 0 & 0 & 1\\
0 & 4 & 0 & 1\\
0 & 0 & 4 & 1\\
2 & 4 & 4 & 1
\end{vmatrix}[/tex]
From here we have:
[tex]\frac{1}{6}\begin{vmatrix}
x_1 & y_1 & z_1 & 1\\
x_2 & y_2 & y_2 & 1\\
x_3 & y_3 & z_3 & 1\\
x_4 & y_4 & y_4 & 1
\end{vmatrix}[/tex]
Finding the determinant of that matrix we have:
[tex]\frac{1}{6} (-64)[/tex] = [tex]\frac{-32}{3}[/tex]