# Dictionary:Triple product

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A triple scalar product is

${\displaystyle \left({\textbf {P}}\times {\textbf {Q}}\right)\cdot {\textbf {R}}=}$ ${\displaystyle {\textbf {R}}\cdot \left({\textbf {P}}\times {\textbf {Q}}\right)=}$ ${\displaystyle -{\textbf {R}}\cdot \left({\textbf {Q}}\times {\textbf {P}}\right)=}$ ${\displaystyle -\left({\textbf {Q}}\times {\textbf {P}}\right)\cdot {\textbf {R}}}$

${\displaystyle =\left|{\begin{array}{ccc}P_{x}&P_{y}&P_{z}\\Q_{x}&Q_{y}&Q_{z}\\R_{x}&R_{y}&R_{z}\end{array}}\right|}$.

A triple vector product is

${\displaystyle \left({\textbf {P}}\times {\textbf {Q}}\right)\times {\textbf {R}}=}$ ${\displaystyle -{\textbf {R}}\times \left({\textbf {P}}\times {\textbf {Q}}\right)=}$ ${\displaystyle {\textbf {R}}\times \left({\textbf {Q}}\times {\textbf {P}}\right)=}$ ${\displaystyle \left({\textbf {R}}\cdot {\textbf {P}}\right){\textbf {Q}}-\left({\textbf {R}}\cdot {\textbf {Q}}\right){\textbf {P}}}$

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