2.
\((1)\)已知\(a=(1,2)\),\(a-4b=(-15,-6)\),则\(a\)与\(b\)的夹角的余弦值为________.
\((2)P\)是长、宽、高分别为\(12\),\(3\),\(4\)的长方体外接球表面上一动点,则\(P\)到长方体各个面所在平面的距离的最大值是________.
\((3)\)设函数\(f(x)\)的定义域为\(D\),如果\(\forall x∈D\),\(\exists y∈D\),使\(\dfrac{f(x)+f(y)}{2}=C(C\)为常数\()\)成立,则称函数\(f(x)\)在\(D\)上的均值为\(C.\)给出下列四个函数:\(①y=x^{2}\);\(②y=2^{x}\);\(③y=\ln x\);\(④y=2\sin x+1.\)则其中满足在其定义域上均值为\(2\)的函数是________.
\((4)\)已知椭圆\(\dfrac{{{x}^{2}}}{{{a}^{2}}}+\dfrac{{{y}^{2}}}{{{b}^{2}}}=1(a > b > 0)\)的左、右焦点分别为\(F_{1}\),\(F_{2}\),过\(F_{1}\)且与\(x\)轴垂直的直线交椭圆于\(A\)、\(B\)两点,直线\(AF_{2}\)与椭圆的另一个交点为\(C\),若\({{S}_{\vartriangle ABC}}=\dfrac{{7}}{{2}}{{S}_{\vartriangle BC{{F}_{2}}}}\),则椭圆的离心率为____________.