Respuesta :

The volume of the parallelepiped with adjacent edges PQ, PR, and PS is 24 cubic units.

What is parallelepiped?

Six parallelograms come together to form a three-dimensional shape called a parallelepiped (the term rhomboid is also sometimes used with this meaning). It is comparable to a parallelogram in the same way that a cube is comparable to a square. In Euclidean geometry, the four concepts—parallelepiped and cube in three dimensions, parallelogram, and square in two dimensions—are specified; however, only parallelograms and parallelepipeds exist in the setting of a more generic affine geometry, where angles are not discriminated.

There are three similar descriptions of a parallelepiped:

  • A polyhedron called a hexahedron, which has six parallelogram-shaped faces
  • Three pairs of parallel faces on a hexahedron, and
  • A prism with a parallelogram as its base.

We have been that  p(−2, 1, 0), q(4, 4, 4), r(1, 4, −1), and s(3, 6, 1) are the adjacent edges of parallelepiped

PQ = Q-P = <6,3,4>

PR = R-P = <3,3.-1>

PS= S-P = <5,5,1>

[ PQ PR PS] = [tex]\begin{vmatrix}6& 3 & 4 \\ 3& 3 &-1 \\ 5 & 5 & 1 \\ \end{vmatrix}\\ \notag&& \\[/tex]

= 6(3+5)-3(3+5)+4(15-15)

= 6×8-3×8+0

=48-24

=24

To learn more about parallelepiped, visit:

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