Respuesta :
The volume of the parallelepiped is 299³ units.
What is parallelepiped?
- A parallelepiped is a three-dimensional character formed by six parallelograms in geometry (the term rhomboid is also sometimes used with this meaning).
- It is analogous to a parallelogram in the same way that a cube is analogous to a square.
- In Euclidean geometry, the 4 concepts—parallelepiped and cube in three dimensions, parallelogram as well as square in two-dimension —are defined, but only parallelograms and parallelepipeds exist in the context of more general affine geometry, in which angles are not differentiated.
So,
The volume of parallelopiped can be calculated using the steps below.
- PQ = Q - Vertex = (-5, -5, 1)
- PR = R - Vertex = (-1, 6, 1)
- PS = S - Vertex = (6, 3, 7)
Now, the volume of parallelopiped is increasing:
[tex]v=\left|\begin{array}{lll}-5 & -5 & 1 \\-1 & 6 & 1 \\6 & 3 & 7\end{array}\right|[/tex]
The matrix's determinant is:
⇒ -5(42 - 3) +5(-7 -6) +1(-3 - 36)
⇒ -5(39) +5(-13) +1(-39)
⇒ -195 -65 -39
⇒ |-299| = 299
Therefore, the volume of the parallelepiped is 299³ units.
Know more about parallelepiped here:
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