question_answer

If \[\overset{\to }{\mathop{A}}\,.\overset{\to }{\mathop{B}}\,\]and \[\overset{\to }{\mathop{C}}\,\]are mutually perpendicular vectors, then find the value of \[\overset{\to }{\mathop{A}}\,.(\overset{\to }{\mathop{B}}\,+\overset{\to }{\mathop{C}}\,)\].                

Answer:

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