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

International Tables for Crystallography (2010). Vol. B, ch. 3.1, p. 405   | 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[link] is one multiplicative operation of two vectors that may be defined; another is the vector product, which is denoted as [{\bf u} \wedge {\bf v}] (or [{\bf u} \times {\bf v}] or [uv]). The vector product of vectors u and v is defined as a vector of length [uv\sin \varphi], where [\varphi] is the angle between the vectors, and of direction perpendicular to both u and v in the sense that u, v and [{\bf u} \wedge {\bf v}] form a right-handed system; [{\bf u} \wedge {\bf v}] is generated by rotating u into v and advancing in the direction of a right-handed screw. The magnitude of [{\bf u} \wedge {\bf v}], given by[|{\bf u} \wedge {\bf v}| = uv \sin \varphi \eqno(3.1.5.1)]is equal to the area of the parallelogram defined by u and v.

It follows from the definition that[{\bf u} \wedge {\bf v} = -{\bf v} \wedge {\bf u}. \eqno(3.1.5.2)]








































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