If \( \overrightarrow{\mathrm{A}}, \overrightarrow{\mathrm{B}} \) and \( \overrightarrow{\mathrm{C}} \) are vectors such that
\( \mathrm{P} \)
W \( |\overrightarrow{\mathrm{B}}|=|\overrightarrow{\mathrm{C}}| \). Prove that
\[
[(\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}) \times(\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{C}})] \times(\overrightarrow{\mathrm{B}} \times \overrightarrow{\mathrm{C}}) \cdot(\overrightarrow{\mathrm{B}}+\overrightarrow{\mathrm{C}})=\overrightarrow{0}
\]
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