If direction ratios of two lines are $5,\,\, - 12,\,13$ and $ - 3,\,4,\,5$ then the angle between them is
→If the function $f$ defined on $\left( {\frac{\pi }{6},\frac{\pi }{3}} \right)$ by $f\,(x)\, = \,\left\{ {\begin{array}{*{20}{c}}
{\frac{{\sqrt 2 \,\cos \,x - \,1}}{{\cot \,x\, - \,1}}\,,\,x\, \ne \,\frac{\pi }{4}}\\
{k,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\, = \frac{\pi }{4}}
\end{array}} \right.$ is continuous, then $k$ is equal to
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