2．
\(( 1 )\)已知向量\(\overrightarrow{a},\overrightarrow{b}\)，满足\(\overrightarrow{a}=\left( 1,3 \right)\)，\(\left( \overrightarrow{a}+\overrightarrow{b} \right)\bot \left( \overrightarrow{a}-\overrightarrow{b} \right)\)，则\(\left| \overrightarrow{b} \right|=\)______．
\(( 2 )\)已知实数\(x,y\)满足\(\begin{cases} & x\leqslant 3 \\ & x+y-3\geqslant 0 \\ & x-y+1\geqslant 0 \\ \end{cases}\)，则\({{x}^{2}}+{{y}^{2}}\)的最小值是 ．
\(( 3 )\)已知圆\(O:{{x}^{2}}+{{y}^{2}}=1.\)圆\({O}{{'}}\)与圆\(O\)关于直线\(x+y-2=0\)对称，则圆\({O}{{'}}\)的方程是__________．
\(( 4 )\)已知数列\(\left\{ a{}_{n} \right\},\left\{ {{b}_{n}} \right\}\)满足\(b{}_{n}=\log {}_{2}a{}_{n},n\in {{N}^{*}}\)，其中\(\left\{ {{b}_{n}} \right\}\)是等差数列，且\({{a}_{9}}{{a}_{2009}}=\dfrac{1}{4}.\)则\({{b}_{1}}+{{b}_{2}}+{{b}_{3}}+\cdot \cdot \cdot +{{b}_{2017}}=\)__________．