|[a b c]| = volume of the parallelepiped with edges a, b, c emanating from a common vertex.

The sign of [a b c] indicates orientation:

• Positive: a, b, c form a right-handed system.
• Negative: a, b, c form a left-handed system.

Related volumes:

• Volume of tetrahedron with three co-terminal edges a, b, c = $\frac{1}{6}$|[a b c]|.
• Volume of tetrahedron with vertices A, B, C, D = $\frac{1}{6}$|[AB AC AD]|.
• The factor 1/6 arises because a tetrahedron occupies 1/6 of the parallelepiped.

If [a b c] = 0, the parallelepiped is flat — the three vectors lie in a common plane (or one is a linear combination of the other two).