Question

The volume of the tetrahedron with vertices at (1,2,3), (4,3,2), (5,2,7), (6,4,8) is

• A. $\frac{22}{3}$
• B. $\frac{11}{3}$
• C. $\frac{1}{3}$
• D. $\frac{16}{3}$

Answer 1

The correct option is D $\frac{16}{3}$

$\left[\overrightarrow{AB}\overrightarrow{AC}\overrightarrow{AD}\right]=\left|\begin{array}{ccc}3& 1& -1\\ 4& 0& 4\\ 5& 2& 5\end{array}\right|=3(0-8)-1(20-20)-1(8-0)=-24-0-8=-32$
Volume of the tetrahedron =$\frac{1}{6}\left(32\right)=\frac{16}{3}$ cubic unit.