Physics - Vectors Question with Solution | TestHub

$\begin{array}{rl}& \cos \theta =\frac{5}{9}\\ & \frac{\vec{a}\cdot \vec{b}}{ab}=\frac{5}{9}\\ & a^2+b^2+2\vec{a}\cdot \vec{b}=2a^2+2b^2-4\vec{a}\cdot \vec{b}\\ & 6\vec{a}\cdot \vec{b}=a^2+b^2\end{array}$ $\begin{array}{rl}& 6\times \frac{5}{9}ab=a^2+b^2\\ & \frac{10}{3}ab=a^2+b^2\&a=nb\\ & \frac{10}{3}n{b}^2=n^2{b}^2+b^2\\ & 3n^2-10n+3=0\\ & n=\frac{1}{3}\text{ and }n=3\end{array}$ integer value $n=3$