The volume of the parallelepiped shown can be calculated by $r_{PQ}*(r_{PR}{r}_{PS}).$ Use the following steps in a script file to calculate the volume.

Define the vectors $r_{PQ},r_{PR},$ and $r_{PS}$ from the positions of points $P,Q,R,$ and S $.$

Determine the volume using MATLAB's built$-$in functions dot and cross.

Given the points:

$P=(4,7,3)$

$Q=(3,2,6)$

$R=(-5,9,2)$

$S=(1,4,8)$

More information:

Here is the $3$ D plot of the paranemepipea uenneu oy ue pomis $r-(4,1,3),Q=(3,2,6),R=(-5,9,2),$ and $S=(1,4,8).$ The vertices are labeled accordingly:

$P(P1)$

Q $($P$2)$

R $($P$3)$

S $($P$4)$

Additional vertices calculated: P$5,$ P$6,$ P$7,$ and P$8($No need in this problem$)$

The parallelepiped is visualized with its faces highlighted in cyan and edges in red. Each vertex is marked with a blue dot and labeled for clarity. This visualization helps to understand the geometric shape and spatial relationship of the points defining the parallelepiped.

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Result