Consider two vectors $\vec{u}=3\hat{i}-\hat{j}$ and $\vec{v}=2\hat{i}+\hat{j}-\lambda\hat{k},\ \lambda>0$. The angle between them is given by $\cos^{-1}!\left(\dfrac{\sqrt{5}}{2\sqrt{7}}\right)$. Let $\vec{v}=\vec{v}_1+\vec{v}_2$, where $\vec{v}_1$ is parallel to $\vec{u}$ and $\vec{v}_2$ is perpendicular to $\vec{u}$. Then the value $\left|\vec{v}_1\right|^{2}+\left|\vec{v}_2\right|^{2}$ is equal to