Answer:
\[\overset{\to }{\mathop{A}}\,.(\overset{\to
}{\mathop{B}}\,+\overset{\to }{\mathop{C}}\,)=\overset{\to
}{\mathop{A}}\,.\overset{\to }{\mathop{B}}\,+\overset{\to
}{\mathop{A}}\,.\overset{\to }{\mathop{C}}\,=AB\cos {{90}^{o}}+AC\cos
{{90}^{o}}=0\]
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