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Parallelepiped
Task number: 2607
Calculate the volume of the parallelepiped determinde by vectors aT=(3,1,1), bT=(2,1,1) and cT=(2,3,2).
(A parallelepiped in R3 contains points that can be expressed as a linear combination αa+βb+γc, where α,β,γ∈⟨0,1⟩.)
Solution
The volume of a parallelepiped is the absolute value of the determinant whose columns are vectors a,b,c, i.e. V=|det.