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## 'Cross with the Scalar Product' printed from http://nrich.maths.org/

Always remember the key geometrical facts about scalar and cross
products for non-zero vectors ${\bf u}$ and ${\bf v}$:

1) ${\bf u}\cdot {\bf v}=0$ if and only if ${\bf u}$ and ${\bf v}$
are perpendicular.

2) ${\bf u}\times {\bf v}=0$ if and only if ${\bf u}$ and ${\bf v}$
are parallel.

3) ${\bf u}\times {\bf v}$ is perpendicular to both ${\bf u}$ and
${\bf v}$.

This problem uses mathematical
concepts covered in the later Further Pure Mathematics A Level
Modules.