If O = (0, 0, 0), P = (4, 3, -5), Q = ( -2,1, -8), cos$\angle \mathrm{POQ}=\frac{\mathrm{a}}{\sqrt{\mathrm{b}}\sqrt{\mathrm{c}}}\mathrm{andb}>\mathrm{c} \mathrm{then} \mathrm{b}-\mathrm{c}=$

$$\begin{gathered} \mathrm{D}.\mathrm{r}’\mathrm{s} \mathrm{of} \mathrm{OP} =\left(4,3,-5\right)=\left({\mathrm{a}}_1,{\mathrm{b}}_1,{\mathrm{c}}_1\right) \mathrm{D}.\mathrm{r}’\mathrm{s} \mathrm{of} \mathrm{OQ}=\left(-2,1,-8\right)=\left({\mathrm{a}}_2,{\mathrm{b}}_2,{\mathrm{c}}_2\right) \\ \mathrm{cos\theta }=\frac{\left|{\mathrm{a}}_1{\mathrm{a}}_2+{\mathrm{b}}_1{\mathrm{b}}_2+{\mathrm{c}}_1{\mathrm{c}}_2\right|}{\sqrt{{\mathrm{a}}_1^2+{\mathrm{b}}_1^2+{\mathrm{c}}_1^2}\sqrt{{\mathrm{a}}_2^2+b_2^2+c_2^2}}\cos \angle \mathrm{POQ}=\frac{\left|-8+3-40\right|}{\sqrt{50}\sqrt{69}}=\frac{45}{\sqrt{69}\sqrt{50}} \\ \Rightarrow \mathrm{b}-\mathrm{c}=69-50, \Rightarrow \mathrm{b}-\mathrm{c}=19 \end{gathered}$$