已知\(\overrightarrow{a}{=}(m{,}1)\)，\(\overrightarrow{b}{=}(4{-}n{,}2)\)，\(m{ > }0\)，\(n{ > }0\)，若\(\overrightarrow{a}{/\!/}\overrightarrow{b}\)，则\(\dfrac{1}{m}{+}\dfrac{8}{n}\)的最小值______ ．

\((1)\)化简\(\overrightarrow{{AC}}{-}\overrightarrow{{BD}}{+}\overrightarrow{{CD}}{-}\overrightarrow{{AB}}= \)______ ．

\((2)\)若非零向量\(\overrightarrow{a}\)，\(\overrightarrow{b}\)满足\({|}\overrightarrow{a}{+}\overrightarrow{b}{|=|}\overrightarrow{a}{-}\overrightarrow{b}{|=}2{|}\overrightarrow{a}{|}\)，则向量\(\overrightarrow{b}\)与\(\overrightarrow{a}{+}\overrightarrow{b}\)的夹角为______．

\((3)\)已知平行四边形\(ABCD\)，\(A(1,1)\)，\(B(3,3)\)，\(C(4,0)\)，则\(D\)点坐标 ______ ．

\((4)\)如图，函数\(y=2\sin (πx+φ)\)，\(x∈R\)，\((\)其中\(0\leqslant φ\leqslant \dfrac{\pi}{2})\)的图象与\(y\)轴交于点\((0,1).\)设\(P\)是图象上的最高点，\(M\)、\(N\)是图象与\(x\)轴的交点，\(\overrightarrow{{PM}}{⋅}\overrightarrow{{PN}}= \)______ ．

已知\(a∈\left[ \dfrac{π}{2},π\right], \overrightarrow{a}=\left(2,-1\right), \overrightarrow{b}=\left(\cos a,\sin a\right), \)且\( \overrightarrow{a}/\!/ \overrightarrow{b} \)．

\((2)\)求\(\cos (\dfrac{5\pi }{6}-2\alpha )\)的值．

\(\Delta {A} {B} {C}\)的内角\({A} \)，\({B} \)，\({C}\)所对的边分别为\(a\)，\(b\)，\(c\)．向量\(\vec{m}=\left( a,\sqrt{3}b \right)\)与\(\vec{n}=\left( \cos {A} ,\sin {B} \right)\)平行．

\((1)\)求\({A} \)；      

 \((2)\)若\(a=\sqrt{7}\)，\(b=2\)求\(\Delta {A} {B} {C}\)的面积．

向量\( \overset{⇀}{a}=( \dfrac{1}{3},\tan α) \)，\( \overset{⇀}{b}=\left(\cos α,1\right) \)，且\( \overset{⇀}{a} /\!/ \overset{⇀}{b} \)，则\(\cos 2α=(\)　　\()\)

下列命题正确的是\(({  })\)

已知向量\(a=(m,4)\)，\(b=(5,-2)\)，且\(a/\!/b\)，则\(m=\)___________．