Volume of a parallelepiped, given 8 verticesGiven 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?

Question

Volume of a parallelepiped, given 8 verticesGiven 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&#039;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?

Julien Zuniga · Accepted Answer

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.

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.

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