共50条信息
如图,在四棱锥\(P-ABCD \)中,\(PA⊥ \)底面\(ABCD\),\(AD⊥AB \),\(AB/\!/DC,AD=DC=AP=2,AB=1 \),点\(E\)为棱\(PC\)的中点.
\((2)\)在线段\(BC\)上是否存在一点\(P\),使\(AP\bot DE\)?证明你的结论.
如图,三棱柱\(ABC-{{A}_{1}}{{B}_{1}}{{C}_{1}}\)中,\({{A}_{1}}C\bot \)底面\(ABC\),\(\angle ACB={120}{}^\circ \),\({{A}_{1}}C=AC=BC=2\),\(D\)为\(AB\)中点.
\(\left( {1} \right)\)求证:\(B{{C}_{1}}/\!/\)平面\({{A}_{1}}CD;\)
\(\left( {2} \right)\)求直线\({{A}_{1}}D\)与平面\({{A}_{1}}{{C}_{1}}B\)所成角的正弦值.
\((\)Ⅰ\()\)证明:\({{A}_{1}}C\bot A{{B}_{1}}\);
\((\)Ⅱ\()\)若\(D\)是棱\(C{{C}_{1}}\)的中点,在棱\(AB\)上是否存在一点\(E\),使\(DE/\!/\)平面\(A{{B}_{1}}{{C}_{1}}\)?证明你的结论.
在平面四边形\(ABCD\)中,\(AB=BD=CD=1,AB\bot BD,CD\bot BD\) ,将\(\Delta ABD\)沿\(BD\)折起,使得平面\(ABD\bot \)平面\(BCD\),如图所示.
\((1)\)求证:\(AB\bot CD\);
\((2)\)若\(M\)为\(AD\)中点,求直线\(AD\)与平面\(MBC\)所成角的正弦值.
如图所示,四棱锥\(P\)\(-\)\(ABCD\)的底面是边长为\(1\)的正方形,\(PA\)\(⊥\)\(CD\),\(PA\)\(=\)\(1\),\(PD\)\(=\)\( \sqrt{2} \),\(E\)为\(PD\)上一点,\(PE\)\(=\)\(2\)\(ED\).
\((1)\)求证:\(PA\)\(⊥\)平面\(ABCD\);
\((2)\)在侧棱\(PC\)上是否存在一点\(F\),使得\(BF\)\(/\!/\)平面\(AEC\)?若存在,指出\(F\)点的位置,并证明;若不存在,说明理由.
如图,已知正三棱柱\(ABC-A_{1}B_{1}C_{1}\)的各棱长均为\(4\),\(E\)是\(BC\)的中点,点\(F\)在侧棱\(CC_{1}\)上,且\(CC_{1}=4CF\)
在正方体\(ABCD-{{A}_{1}}{{B}_{1}}{{C}_{1}}{{D}_{1}}\)中,\(O\)是\(AC\)的中点,\(E\)是线段\({{D}_{1}}O\)上一点,且\({{D}_{1}}E=\lambda EO\).
\((1)\)若\(\lambda =1\),求异面直线\(DE\)与\(C{{D}_{1}}\)所成角的余弦值;
\((2)\)若平面\(CDE\bot \)平面\(C{{D}_{1}}O\),求\(\lambda \)的值.
如图,四棱锥\(P-ABCD\)中,\(ABCD\)为矩形,\(\Delta PAD\)为等腰直角三角形,\(\angle APD={{90}^{\circ }}\),面\(PAD⊥\)面\(ABCD\),且\(AB=1,AD=2\),\(E,F\)分别为\(PC\)和\(BD\)的中点.
\((\)Ⅰ\()\)证明:\(EF/\!/\)面\(PAD\);
\((\)Ⅱ\()\)求锐二面角\(B-PD-C\)的余弦值.
在平面四边形\(ABCD\)中,\(AB\)\(=\)\(BD\)\(=\)\(CD\)\(=1\),\(AB\)\(⊥\)\(BD\),\(CD\)\(⊥\)\(BD\)\(.\)将\(\triangle \)\(ABD\)沿\(BD\)折起,使得平面\(ABD\)\(⊥\)平面\(BCD\),如图所示.
\((1)\)求证:\(AB\)\(⊥\)\(CD\);\((2)\)若\(M\)为\(AD\)中点,求直线\(AD\)与平面\(MBC\)所成角的正弦值.
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