View source for Pseudo-scalar product

''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" />''

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" />:

<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>

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.

See [[Vector algebra|Vector algebra]].



====Comments====
The pseudo-scalar product of two vectors gives the length of the [[Vector product|vector product]] of these two vectors.