Question
Evaluate the product $\left( {3\vec a - 5\vec b} \right).\left( {2\vec a + 7\vec b} \right)$
$=6{\left| {\vec a} \right|^2} + 11\vec a.\vec b - 35{\left| {\vec b} \right|^2}$
$\left[ {\because \vec a.\vec a = {{\left| {\vec a} \right|}^2},\vec b.\vec b = {{\left| {\vec b} \right|}^2},\vec a.\vec b = \vec b.\vec a} \right]$
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