Find the volume of the parallelepiped with one vertex at the origin and adjacent

illusiia 2021-09-22 Answered

Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1,3,0),(2,0,2),and(1,3,1).

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Expert Answer

mhalmantus
Answered 2021-09-23 Author has 106 answers

Setup the matrix A, where the columns are the vectors given.
A=[121303021]
The volume of the parallelepiped is equal to the absolute value of the determinant of A.
Volume =|det(A)|
So lets calculate the determinant. Expanding along the first column (because A3,1=0 gives us two terms, but i'll show it for clarification)gives us to shown calculation.
A=|121303021|=|0321|3|2121|+0|2103|=612=18
Volume of the parallelepiped is 18.
Results:
Volume of the parallelepiped is 18.

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