Let $\vec{a},\vec{b},and\vec{c}and{\vec{a}}^{{}^{\prime }},{\vec{b}}^{{}^{\prime }},{\vec{c}}^{\prime }$ are reciprocal system of vectors, then prove that ${\vec{a}}^{{}^{\prime }}\times {\vec{b}}^{{}^{\prime }}+{\vec{b}}^{{}^{\prime }}\times {\vec{c}}^{{}^{\prime }}+{\vec{c}}^{{}^{\prime }}\times {\vec{a}}^{{}^{\prime }}=\frac{\vec{a}+\vec{b}+\vec{c}}{\left[\vec{a}\vec{b}\vec{c}\right]}$ .

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