\((1)\)设向量\(\overrightarrow{a}=(m,1)\overrightarrow{b}=(1,2)\),且\({{\left| \overrightarrow{a}+\overrightarrow{b} \right|}^{2}}={{\left| \overrightarrow{a} \right|}^{2}}+{{\left| \overrightarrow{b} \right|}^{2}}\),则\(m=\)___________.
\((2){{(2x+\sqrt{x})}^{5}}\)的展开式中,\({{x}^{3}}\)的系数是______\(.(\)用数字填写答案\()\)
\((3)\)已知\(f(x)\)是定义在\(R\)上的偶函数,且在区间\((-\infty ,0)\)上单调递增\(.\)若实数\(a\)满足\(f\left({2}^{\left|a-1\right|}\right) > f\left(- \sqrt{2}\right) \),则\(a\)的取值范围是_____________.
\((4)\)已知椭圆\(\Gamma :\dfrac{{{x}^{2}}}{{{a}^{2}}}+\dfrac{{{y}^{2}}}{{{b}^{2}}}=1(a > b > 0)\)的右焦点为\(F(3,0)\),上、下顶点分别为\(A,B\),直线\(AF\)交\(\Gamma \)于另一点\(M\),若直线\(BM\)交\(x\)轴于点\(N(12,0)\),则\(\Gamma \)的离心率是_____.