International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shumeli

International Tables for Crystallography (2006). Vol. B, ch. 3.1, p. 349   | 1 | 2 |

Section 3.1.5. Vector product

D. E. Sandsa*

aDepartment of Chemistry, University of Kentucky, Chemistry–Physics Building, Lexington, Kentucky 40506-0055, USA
Correspondence e-mail: sands@pop.uky.edu

3.1.5. Vector product

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The scalar product defined in Section 3.1.2 is one multiplicative operation of two vectors that may be defined; another is the vector product, which is denoted as (or or [uv]). The vector product of vectors u and v is defined as a vector of length , where is the angle between the vectors, and of direction perpendicular to both u and v in the sense that u, v and form a right-handed system; is generated by rotating u into v and advancing in the direction of a right-handed screw. The magnitude of , given by is equal to the area of the parallelogram defined by u and v.

It follows from the definition that