Step 1

\(p(3,\ 0,\ 1),\)

\(Q(-1,\ 2,\ 5),\)

\(R(5,\ 1,\ -1),\)

\(S(0,\ 4,\ 2)\)

\(PQ=Q-P=\langle-4,\ 2,\ 4\rangle\)

\(PR=R-P=\langle2,\ 1,\ -2\rangle\)

\(PS=S-P =\langle-3,\ 4,\ 1\rangle\)

\([PQ\ PR\ PS]=\left|\begin{matrix}-4 & 2 & 4 \\ 2 & 1 & -2 \\ -3 & 4 & 1\end{matrix}\right|\)

\(=-4(9)-2(-4)+4(11)\)

\(=-36+8+44=16\)

volume of the parallelepiped with adjacent edges PQ, PR, and \(PS=16\) cubic units.

\(p(3,\ 0,\ 1),\)

\(Q(-1,\ 2,\ 5),\)

\(R(5,\ 1,\ -1),\)

\(S(0,\ 4,\ 2)\)

\(PQ=Q-P=\langle-4,\ 2,\ 4\rangle\)

\(PR=R-P=\langle2,\ 1,\ -2\rangle\)

\(PS=S-P =\langle-3,\ 4,\ 1\rangle\)

\([PQ\ PR\ PS]=\left|\begin{matrix}-4 & 2 & 4 \\ 2 & 1 & -2 \\ -3 & 4 & 1\end{matrix}\right|\)

\(=-4(9)-2(-4)+4(11)\)

\(=-36+8+44=16\)

volume of the parallelepiped with adjacent edges PQ, PR, and \(PS=16\) cubic units.