Scalar product: Difference between revisions
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<div class="definition"><div class="short_definition">( | <div class="definition"><div class="short_definition">(''Also called'' dot product, direct product, inner product.) A [[scalar]] equal to the product of the magnitudes of any two [[vectors]] and the cosine of the angle θ between their positive directions.</div><br/> <div class="paragraph">For two vectors '''A''' and '''B''', the scalar product is most commonly written '''A''' · '''B''', read "'''A''' dot '''B'''," and occasionally as ('''AB'''). If the vectors '''A''' and '''B''' have the components ''A''<sub>x</sub>, ''B''<sub>x</sub>, ''A''<sub>y</sub>, ''B''<sub>y</sub>, and ''A''<sub>z</sub>, ''B''<sub>z</sub> along rectangular Cartesian ''x'', ''y'', and ''z'' axes, respectively, then <div class="display-formula"><blockquote>[[File:ams2001glos-Se7.gif|link=|center|ams2001glos-Se7]]</blockquote></div> If a scalar product is zero, one of the vectors is zero or else the two are perpendicular. <br/>''See'' [[vector product]].</div><br/> </div> | ||
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Revision as of 15:03, 20 February 2012
scalar product
(Also called dot product, direct product, inner product.) A scalar equal to the product of the magnitudes of any two vectors and the cosine of the angle θ between their positive directions.
For two vectors A and B, the scalar product is most commonly written A · B, read "A dot B," and occasionally as (AB). If the vectors A and B have the components Ax, Bx, Ay, By, and Az, Bz along rectangular Cartesian x, y, and z axes, respectively, then If a scalar product is zero, one of the vectors is zero or else the two are perpendicular.
See vector product.
See vector product.
