Let $\overline{\mathrm{r}}$ be the position vector of a point in Cartesian OXY plane such that $\overline{\mathrm{r}}\cdot (10\widehat{\mathrm{j}}-8\widehat{\mathrm{i}}-\overrightarrow{\mathrm{r}})=40,max\left\{|\overrightarrow{\mathrm{r}}+2\widehat{\mathrm{i}}-3\widehat{\mathrm{j}}{|}^2\right\}=\mathcal{\text{l}}$ and $min\left\{|\overrightarrow{\mathrm{r}}+2\widehat{\mathrm{i}}-3\widehat{\mathrm{j}}{|}^2\right\}=\mathrm{m}$. A tangent line is drawn to the curve $\mathrm{y}=\frac{8}{{\mathrm{x}}^2}$ at the point $A$ with abscissa 2. The drawn tangent cuts the $x-$axis at $B$, then