Consider two vectors u =3 i - j and v =2 i + j -λ k , λ 0 . The...

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