Pseudo-scalar product

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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.


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:
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article