\(( 1 )\)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\({{b}_{1}}+{{b}_{2}}+{{b}_{3}}+\cdot \cdot \cdot +{{b}_{2017}}=\)__________．

若\(\left|a+b\right|=\left|a-b\right| \)，则向量\(a\)，\(b\)的夹角是             ．

已知椭圆\(+\)\(y\)\({\,\!}^{2}=1\)，\(F\)\({\,\!}_{1}\)，\(F\)\({\,\!}_{2}\)分别是椭圆的左，右焦点，\(c\)为半焦距，\(P\)为直线\(x\)\(=2\)上一点，直线\(PF\)\({\,\!}_{1}\)，\(PF\)\({\,\!}_{2}\)与圆\(x\)\({\,\!}^{2}+\)\(y\)\({\,\!}^{2}=1\)的另外一个交点分别为\(M\)，\(N\)两点．

\((\)Ⅰ\()\)椭圆上是否存在一点\(Q\)，使得\(∠\)\(F\)\({\,\!}_{1}\)\(QF\)\({\,\!}_{2}=\)？若存在，求出\(Q\)点坐标，若不存在，请说明理由；

\((\)Ⅱ\()\)求证：直线\(MN\)恒过一定点．

已知\(\left| \overset{⇀}{a}\right|=4,\left| \overset{⇀}{b}\right|=8 \)，\( \overset{⇀}{a} \)与\( \overset{⇀}{b} \)的夹角为\(\dfrac{2\pi }{3}\) ．

\((\)Ⅰ\()\)求\(\left| \overset{⇀}{a}+ \overset{⇀}{b}\right| \)；       

\((\)Ⅱ\()\)求\(k\)为何值时，\(\left( \overset{⇀}{a}+2 \overset{⇀}{b}\right)⊥\left(k \overset{⇀}{a}- \overset{⇀}{b}\right) \)