Parallelepiped

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 ${\vec {a}}$, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{b}} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{c}} is given by the triple scalar product Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{a} \cdot (\vec{b} \times \vec{c})} .