已知\(A\left( 0,1 \right)\)，\(B\left( \sqrt{2},0 \right)\)，\(O\)为坐标原点，动点\(P\)满足\(\left| \overrightarrow{OP} \right|=2\)，则\(\left| \overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OP} \right|\)的 最小值为(    )

\(\Delta ABC\)中，已知\(\angle C=\dfrac{\pi }{2}\)，\(\left| \overrightarrow{AC} \right| < \left| \overrightarrow{BC} \right|\)，\(\overrightarrow{CO}=\dfrac{1}{2}\lambda \overrightarrow{CA}+(1-\lambda )\overrightarrow{CB}(0 < \lambda < 1)\)，则\(\left| \overrightarrow{CO} \right|\)取最小时有

化简\(( \overrightarrow{AB}- \overrightarrow{CD})-( \overrightarrow{AC}- \overrightarrow{BD}) \)__________\(;\)

在平面直角坐标系\(xOy\)中，已知点\(A(-1,-2),B(2,3),C(-2,-1)\)．

\((1)\)求以线段\(AB,AC\)为邻边的平行四边形两条对角线的长

\((2)\)设实数\(t\)满足\((\overrightarrow{AB}-t\overrightarrow{OC})\bullet \overrightarrow{OC}=0\)，求\(t\)的值

\((1)\)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，\(\overrightarrow{{PM}}{⋅}\overrightarrow{{PN}}= \)______ ．

若\(O\)为\({\triangle }{ABC}\)所在平面内任一点，且满足\((\overrightarrow{{OB}}{-}\overrightarrow{{OC}}){⋅}(\overrightarrow{{OB}}{+}\overrightarrow{{OC}}{-}2\overrightarrow{{OA}}){=}0\)，则\({\triangle }{ABC}\)的形状为(    )