Question

If the volume of tetrahedron whose vertices are $A(0,1,-2),B(2,3,4),C(2,1,0),D(1,1,1)$ is $V,$ then value of $3V$ is

Answer 1

Volume of tetrahedron is given by,
$V=\frac{1}{6}\left|\left|\begin{array}{ccc}{x}_2-x_1& y_2-y_1& z_2-z_1\\ x_3-x_1& y_3-y_1& z_3-z_1\\ x_4-x_1& y_4-y_1& z_4-z_1\end{array}\right|\right|$
$\Rightarrow V=\frac{1}{6}\left|\left|\begin{array}{ccc}2& 2& 6\\ 2& 0& 2\\ 1& 0& 3\end{array}\right|\right|=\frac{1}{6}\times 8=\frac{4}{3}$ cu.units
$\therefore 3V=4$