Question

Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS. p(3,\ 0,\ 1) Q(-1,\ 2,\ 5) R(5,\ 1,\ -1) S(0,\ 4,\ 2)

Trigonometric equation and identitie
ANSWERED
asked 2021-05-12
Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS.
\(p(3,\ 0,\ 1)\)
\(Q(-1,\ 2,\ 5)\)
\(R(5,\ 1,\ -1)\)
\(S(0,\ 4,\ 2)\)

Answers (1)

2021-05-13
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.
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