The direction cosines of a line which makes equal angles with the coordinate axes are

Let $$O$$ be the origin and $$P$$ be a point which is at a distance of 3 units from the origin. If the direction ratios of $$\overline{O P}$$ are $$(1,-2,-2)$$, then the coordinates of $$P$$ are

$$\lim _\limits{z \rightarrow 1} \frac{z^{(1 / 3)}-1}{z^{(1 / 6)}-1}$$ is equal to

$$f(x)=\left\{\begin{array}{cc} \frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}}, & x \neq 0 \\ K \log 2 \log 3, & x=0 \end{array}\right.$$

Find the value of $$k$$ for which the function $$f$$ is continuous.