6.
\((1)\)已知向量\(a=\left( 8,x \right),b=\left( x,2 \right)\),若\(a/\!/b\),则\(x\)的值为__________.
\((2)\)函数\(f(x)=\dfrac{\sqrt{{{\log }_{3}}(x+2)}}{x-1}\)的定义域为____________________.
\((3)\)已知函数\(\tan \alpha \),\(\dfrac{1}{\tan \alpha }\)是关于\(x\)的方程\({{x}^{2}}-kx+{{k}^{2}}-3=0\)的两个实根,且\(\pi < \alpha < \dfrac{3\pi }{2}\),则\(\cos \alpha +\sin \alpha =\)____________.
\((4)\)已知函数\(f(x)=\begin{cases} & \left| x+1 \right|,x\leqslant 0 \\ & \left| {{\log }_{2}}x \right|,x > 0 \end{cases}\),若方程\(f(x)=a\)有四个不同解\({{x}_{1}},{{x}_{2}},{{x}_{3}},{{x}_{4}}\),且\({{x}_{1}} < {{x}_{2}} < {{x}_{3}} < {{x}_{4}}\),则\({{x}_{3}}({{x}_{1}}+{{x}_{2}})+\dfrac{1}{{{x}_{3}}^{2}{{x}_{4}}}\)的取值范围是___________________.