Question

The volume of the tetrahedron whose vertices are $(0,1,2),(3,0,1),(4,3,6)$ and $(2,3,2)$ is equal to

• A. $1$
• B. $6$
• C. $36$
• D. $216$

Answer 1

The correct option is B $6$

Given: $(0,1,2),(3,0,1),(4,3,6)$ and $(2,3,2)$
Volume of tetrahedron is given by,
$V=\frac{1}{6}\left|\begin{array}{ccc}{x}_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\\ x_4-x_1& y_4-y_1& z_4-z_1\end{array}\right|$
$V=\frac{1}{6}\left|\begin{array}{ccc}3& -1& -1\\ 4& 2& 4\\ 2& 2& 0\end{array}\right|=\frac{1}{6}\left(36\right)=6$