$ \Rightarrow \quad 7|\vec a{|^2} + 16\vec a \cdot \vec b - 15|\vec b{|^2} = 0$ ........$(i)$
$(\vec{a}-5 \vec{b}) \cdot(7 \vec{a}+3 \vec{b})=0$
$ \Rightarrow \quad 7|\vec a{|^2} - 32\vec a \cdot \vec b - 15|\vec b{|^2} = 0$ .......$(ii)$
$\left( {\rm{i}} \right) - ({\rm{ii) }} \Rightarrow 48\vec a \cdot \vec b = 0\quad {\rm{ or }}\quad \vec a \bot \vec b$
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વિધાન $1:$ ${\rm{tr}}\left( A \right) = 0$
વિધાન $2:$ $\det \left( A \right) = 1$