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Difference between revisions of "Pseudo-scalar product"

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''skew product, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075830/p0758301.png" />, of non-zero vectors <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075830/p0758302.png" /> and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075830/p0758303.png" />''
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The product of their moduli by the sine of the angle <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075830/p0758304.png" /> of positive (anti-clockwise) rotation from <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075830/p0758305.png" /> to <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075830/p0758306.png" />:
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<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075830/p0758307.png" /></td> </tr></table>
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''skew product,  $  \mathbf a \lor \mathbf b $,
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of non-zero vectors  $  \mathbf a $
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and  $  \mathbf b $''
  
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If <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075830/p0758308.png" /> and (or) <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/p/p075/p075830/p0758309.png" />, then the pseudo-scalar product is assumed to be zero.
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The product of their moduli by the sine of the angle  $  \phi $
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of positive (anti-clockwise) rotation from  $  \mathbf a $
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to  $  \mathbf b $:
  
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See [[Vector algebra|Vector algebra]].
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$$
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\mathbf a \lor \mathbf b  = \
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| \mathbf a | \cdot | \mathbf b | \cdot \sin  \phi .
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$$
  
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If  $  \mathbf a = 0 $
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and (or)  $  \mathbf b = 0 $,
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then the pseudo-scalar product is assumed to be zero.
  
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See [[Vector algebra|Vector algebra]].
  
 
====Comments====
 
====Comments====
 
The pseudo-scalar product of two vectors gives the length of the [[Vector product|vector product]] of these two vectors.
 
The pseudo-scalar product of two vectors gives the length of the [[Vector product|vector product]] of these two vectors.

Latest revision as of 08:08, 6 June 2020


skew product, $ \mathbf a \lor \mathbf b $, of non-zero vectors $ \mathbf a $ and $ \mathbf b $

The product of their moduli by the sine of the angle $ \phi $ of positive (anti-clockwise) rotation from $ \mathbf a $ to $ \mathbf b $:

$$ \mathbf a \lor \mathbf b = \ | \mathbf a | \cdot | \mathbf b | \cdot \sin \phi . $$

If $ \mathbf a = 0 $ and (or) $ \mathbf b = 0 $, then the pseudo-scalar product is assumed to be zero.

See Vector algebra.

Comments

The pseudo-scalar product of two vectors gives the length of the vector product of these two vectors.

How to Cite This Entry:
Pseudo-scalar product. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Pseudo-scalar_product&oldid=48352
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article
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