共50条信息
已知点\(P\)是棱长等于\(2\)的正方体\(ABCD-A_{1}B_{1}C_{1}D_{1}\)内部的一动点,且\(|\overrightarrow{PA}|=2\),则当\(\overrightarrow{P{{C}_{1}}}\cdot \overrightarrow{P{{D}_{1}}}\)的值达到最小时,\(\overrightarrow{P{{C}_{1}}}\)与\(\overrightarrow{P{{D}_{1}}}\)的夹角大小为________.
空间直角坐标系中,已知\(A(2,1,3)\),\(B({-}2 ,3,1)\),点\(A\)关于\(xOy\)平面对称的点为\(C\),则\(B\),\(C\)两点间的距离为\((\) \()\)
在如图所示的几何体中,四边形\(BB_{1}C_{1}C\)是矩形,\(BB_{1}⊥\)平面\(ABC\),\(A_{1}B_{1}/\!/AB\),\(AB=2A_{1}B_{1}\),\(E\)是\(AC\)的中点.
\((1)\)求证:\(A_{1}E/\!/\)平面\(BB_{1}C_{1}C\);
\((2)\)若\(AC=BC=2\sqrt{2}\),\(AB=2BB_{1}=2\),求二面角\(A—BA_{1}—E\)的余弦值.
如图,在正方体\(ABCD-{A}_{1}{B}_{1}{C}_{1}{D}_{1} \)中,\(E\)为线段\(A_{1}C_{1}\)的中点,则异面直线\(DE\)与\(B_{1}C\)所成角的大小为( )
如图,四边形\(ABCD\)为正方形,\(PD\bot \)平面\(ABCD\), \(PD=\sqrt{3}AD\),\(AE\bot PC\)于点\(E\),\(EF/\!/CD\),交\(PD\)于点\(F\).
\((1)\)证明:平面\(ADE\bot \)平面\(PBC\);
\((2)\)求二面角\(D-AE-F\)的余弦值.
进入组卷