\((1)\)已知向量\( \overset{→}{a} =(1,\)\(m\)\()\)，\( \overset{→}{b} =(\)\(m\)，\(m\)\(-3)\)，若\( \overset{→}{a}⊥ \overset{→}{b} \)，则\(m\)\(= \)______．

\((2)\)已知\(\sin \)\(( \dfrac{π}{3} \) \(-α)= \dfrac{1}{3} (0 < α < \dfrac{π}{2} \) \()\)，则\(\sin \)\(( \dfrac{π}{6} \) \(+α)= \)______．

\((3)\)已知\(\triangle ABC\)是边长为\(2\)的等边三角形，则\( \overset{→}{AB}· \overset{→}{BC} = \)______．

\((4)\)设\(\triangle ABC\)的内角\(A\)，\(B\)，\(C\)，所对的边分别是\(a\)，\(b\)，\(c\)\(.\)若\(a\)\({\,\!}^{2}+\)\(b\)\({\,\!}^{2}-\)\(c\)\({\,\!}^{2}+\)\(ab\)\(=0\)，则角\(C= \)______．

若\(\left| \overset{→}{a}\right|=1,\left| \overset{→}{b}\right|=2 \)，且\(\left( \overset{→}{a}+ \overset{→}{b}\right)⊥ \overset{→}{a} \)，则\( \overset{→}{a} \)与\( \overset{→}{b} \)的夹角是        

已知向量\( \overset{→}{a}=(-3,1) \)，\( \overset{→}{b}=(x,6) \)，若\( \overset{→}{a}⊥ \overset{→}{b} \)，则\(x\)等于           

已知\(\overrightarrow{a},\overrightarrow{b}\)是平面向量，如果\(\left| \overrightarrow{a} \right|=\sqrt{6},\left| \overrightarrow{b} \right|=\sqrt{3},\left( \overrightarrow{a}+2\overrightarrow{b} \right)\bot \left( 2\overrightarrow{a}-\overrightarrow{b} \right)\) ，那么\(\overrightarrow{a}\)与\(\overrightarrow{b}\)的数量积    等于           

已知向量\( \overset{→}{a}=(\sin θ,-2) \)与\( \overset{→}{b}=(1,\cos θ) \)互相垂直，其中\(θ∈(0, \dfrac{π}{2}) \)。

\((1)\)求\(\sin θ\)和\(\cos θ\)的值；

\((2)\)若\(\sin (θ-φ)= \dfrac{ \sqrt{10}}{10} \)，\(0 < φ < \dfrac{π}{2} \)，求\(\sin \varphi \)的值。

\(.\)已知向量\(\overrightarrow{m}=(\cos \alpha ,1-\sin \alpha ),\overrightarrow{n}=(-\cos \alpha ,\sin \alpha )(\alpha \in R)\)

\((1)\)若\(\overrightarrow{m}\bot \overrightarrow{n}\)，求角\(\alpha \)的值； 

\((2)\)若\(|\overrightarrow{m}-\overrightarrow{n}|=\sqrt{3}\)，求\(\cos 2\alpha \)的值．