本题目来源于试卷: VectorsVectors，类别为 IB数学
[问答题]
$\mathrm{O}$,$ \mathrm{A}$, $\mathrm{B}$ and C are distinct points such that $\overrightarrow{\mathrm{OA}}=\mathbf{a}, \overrightarrow{\mathrm{OB}}=\mathbf{b}$ and $\overrightarrow{\mathrm{OC}}=\mathbf{c}$ . It is given that $ \mathbf{a}$ is perpendicular to $ \mathbf{b}$4 and $\mathbf{c}$ .
Prove that $ \mathbf{a}$ is perpendicular to $\overrightarrow{\mathrm{BC}}$ .
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