If the angle between the lines (x -5)/(α)=(y +2)/-5=(z +24/5)/(β) and x/1=y/0=z/1 is (π)/4, find the relation between α and β.

$$\cos \frac{\pi}{4}=\frac{|\alpha \cdot 1+0+\beta|}{\sqrt{\alpha^{2}+\beta^{2}+25} \sqrt{2}} \Rightarrow \frac{1}{\sqrt{2}}=\frac{|\alpha+\beta|}{\sqrt{\alpha^{2}+\beta^{2}+25} \sqrt{2}} $$ Squaring both sides, we get $$\begin{aligned} & \alpha^{2}+\beta^{2}+2 \alpha \beta=\alpha^{2}+\beta^{2}+25 \\ & \Rightarrow \alpha \beta=\frac{25}{2} \end{aligned} $$