# Difference between revisions of "Parallelepiped"

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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 | + | 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]] |

## Latest revision as of 14:21, 14 December 2016

A **parallelepiped** (pronounced PAH-RA-LELL-PIE-PID) is a geometric shape that one obtains from three orthogonal vectors 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 products and dot products. The volume of a parallellepiped with sides , and is given by the triple scalar product .