如圖,正方體
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的棱長為1,點(diǎn)
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在側(cè)面
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及其邊界上運(yùn)動,并且總保持
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平行平面
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,則動點(diǎn)P的軌跡的長度是 _______
.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
如圖,在直三棱柱ABC-A
1B
1C
1中,底面△ABC為等腰直角三角形,∠B = 90
0,D為棱BB
1上一點(diǎn),且面DA
1 C⊥面AA
1C
1C.求證:D為棱BB
1中點(diǎn);(2)
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為何值時,二面角A -A
1D - C的平面角為60
0.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
如圖,在四棱錐
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中,底面
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為平行四邊形,
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底面
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,
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,
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,
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,
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,E在棱
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上, (Ⅰ) 當(dāng)
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時,求證:
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平面
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; (Ⅱ) 當(dāng)二面角
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的大小為
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時,求直線
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與平面
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所成角的正弦值.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
如圖,四棱錐
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中,
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面
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,底面
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為矩形,
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分別是
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的中點(diǎn),
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,
(1)求證:
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面
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;
(2)求證:
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面
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;
(3)求四棱錐
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的表面積。
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
已知
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是邊長為
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的正方形ABCD的中心,點(diǎn)E、F分別是AD、BC的中點(diǎn),沿對角線AC把正方形ABCD折成直二面角D-AC-B;
(Ⅰ)求∠EOF的大�。�
(Ⅱ)求二面角E-OF-A的余弦值;
(Ⅲ)求點(diǎn)D到面EOF的距離.
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
如圖所示,在長方體OABC-O
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A
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B
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C
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中,|OA|=2,|AB|=3,|AA
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|=2,E是BC的中點(diǎn)。
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(1)求直線AO
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與B
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E所成角的大小;
(2)作O
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D⊥AC于D。求點(diǎn)O
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到點(diǎn)D的距離。
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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
四、附加題:本大題共2小題,每小題10分,共20分。
(20)(本小題滿分10分)
已知
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是邊長為1的正方形,
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分別為
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上的點(diǎn),且
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沿
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將正方形折成直二面角
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.
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(I)求證:平面
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平面
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;
(II)設(shè)
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點(diǎn)
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與平面
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間的距離為
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,試用
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表示
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.
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科目:高中數(shù)學(xué)
來源:不詳
題型:單選題
已知
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,則
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的取值范圍是( )
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科目:高中數(shù)學(xué)
來源:不詳
題型:填空題
若
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,
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,
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是平面
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內(nèi)的三點(diǎn),設(shè)向量
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,且
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,則
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________________。
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