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A '''parallelepiped''' (pronounced PAH-RA-LELL-PIE-PID) is a [[geometric]] [[shape]] that one obtains from three [[orthogonal]] [[vector]]s and their sums forming a slanted box. A [[cube]] is a special case of a parallelpiped, namely where all the vectors are [[perpendicular]] to each other and have equal magnitude. The sides of the parallelepiped form [[parallel]] "pipes" (sides).

A '''parallelepiped''' (pronounced PAH-RA-LELL-PIE-PID) is a [[geometric]] [[shape]] that one obtains from three [[orthogonal]] [[vector]]s and their sums forming a slanted box. A [[cube]] is a special case of a parallelpiped, namely where all the vectors are [[perpendicular]] to each other and have equal magnitude. The sides of the parallelepiped form [[parallel]] "pipes" (sides).

Students normally encounter parallellepipeds in [[vector calculus]], in the same introductory module that deals with [[cross product]]s and [[dot product]]s.

Students normally encounter parallellepipeds in vector calculus, in the same introductory module that deals with [[cross product]]s and [[dot product]]s. The [[volume]] of a parallellepiped with sides <math>\vec{a}</math>, <math>\vec{b}</math> and <math>\vec{c}</math> is given by the triple scalar product <math>\vec{a} \cdot (\vec{b} \times \vec{c})</math>.

[[Category:Geometry]][[Category:Calculus]]

[[Category:Geometry]]

[[Category:Calculus]]