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

International Tables for Crystallography (2010). Vol. B, ch. 3.1, p. 404   | 1 | 2 |

Section 3.1.3. Length of a vector

D. E. Sandsa*

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

3.1.3. Length of a vector

| top | pdf |

By (3.1.2.1)[link], the scalar product of a vector with itself is[{\bf v} \cdot {\bf v} = (v)^{2}. \eqno(3.1.3.1)]The length of v is, therefore, given by[v = (v^{i} v^{\,j} g_{ij})^{1/2}. \eqno(3.1.3.2)]Computation of lengths in a generalized rectilinear coordinate system is thus simply a matter of evaluating the double summation [v^{i}v^{\,j}g_{ij}] and taking the square root.








































to end of page
to top of page