三重積 (ベクトル解析)
{ ( a ⋅ c ) b − ( b ⋅ c ) a } ⋅ d = { ( a × b ) × c } ⋅ d {\displaystyle \left\{({\boldsymbol {a}}\cdot {\boldsymbol {c}}){\boldsymbol {b}}-({\boldsymbol {b}}\cdot {\boldsymbol {c}}){\boldsymbol {a}}\right\}\cdot {\boldsymbol {d}}=\{({\boldsymbol {a}}\times {\boldsymbol {b}})\times {\boldsymbol {c}}\}\cdot {\boldsymbol {d}}}
∴ ( a × b ) × c = ( a ⋅ c ) b − ( b ⋅ c ) a {\displaystyle \therefore ~({\boldsymbol {a}}\times {\boldsymbol {b}})\times {\boldsymbol {c}}=({\boldsymbol {a}}\cdot {\boldsymbol {c}}){\boldsymbol {b}}-({\boldsymbol {b}}\cdot {\boldsymbol {c}}){\boldsymbol {a}}}
となる。
エディントンのイプシロンを使うと三重積は以下のように計算できる。