Let $$\lambda_{1}, \lambda_{2}$$ be the values of $$\lambda$$ for which the points $$\left(\frac{5}{2}, 1, \lambda\right)$$ and $$(-2,0,1)$$ are at equal distance from the plane $$2 x+3 y-6 z+7=0$$. If $$\lambda_{1} > \lambda_{2}$$, then the distance of the point $$\left(\lambda_{1}-\lambda_{2}, \lambda_{2}, \lambda_{1}\right)$$ from the line $$\frac{x-5}{1}=\frac{y-1}{2}=\frac{z+7}{2}$$ is ____________.

Consider a circle $$C_{1}: x^{2}+y^{2}-4 x-2 y=\alpha-5$$. Let its mirror image in the line $$y=2 x+1$$ be another circle $$C_{2}: 5 x^{2}+5 y^{2}-10 f x-10 g y+36=0$$. Let $$r$$ be the radius of $$C_{2}$$. Then $$\alpha+r$$ is equal to _________.

The largest natural number $$n$$ such that $$3^{n}$$ divides $$66 !$$ is ___________.

An air bubble of volume $$1 \mathrm{~cm}^{3}$$ rises from the bottom of a lake $$40 \mathrm{~m}$$ deep to the surface at a temperature of $$12^{\circ} \mathrm{C}$$. The atmospheric pressure is $$1 \times 10^{5} \mathrm{~Pa}$$ the density of water is $$1000 \mathrm{~kg} / \mathrm{m}^{3}$$ and $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$$. There is no difference of the temperature of water at the depth of $$40 \mathrm{~m}$$ and on the surface. The volume of air bubble when it reaches the surface will be: