Given the eight vertices (0,0,0), (3,0,0), (0,5,1), (3,5,1), (2,0,5), (5,0,5), (2,5,6), and (5,5,6), find the volume of the parallelepiped.

Zack Chase 2022-09-24 Answered
Volume of a parallelepiped, given 8 vertices
Given the eight vertices (0,0,0), (3,0,0), (0,5,1), (3,5,1), (2,0,5), (5,0,5), (2,5,6), and (5,5,6), find the volume of the parallelepiped.
I'm having trouble finding the 1 vertex and 3 vectors needed to find the volume. The closest four vertexes I found so far are (0,0,0),(3,0,0),(0,5,1),(3,5,1)...is using those four vertexes correct? Any starting hints to point me in the right direction?
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Answers (1)

Julien Zuniga
Answered 2022-09-25 Author has 7 answers
Explanation:
If the origo is among them, the set of vertices of a parallelepiped is of the form { 0 ,   a ,   b ,   c ,   a + b ,   a + c ,   b + c ,   a + b + c } for some vectors a,b,c.
Then write the coordinates of these a,b,c in a matrix and calculate its determinant.
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