(14分)如圖正方體
ABCD-
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中,
E、
F、
G分別是
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、
AB、
BC的中點.
(1)證明:
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⊥平面
AEG;
(2)求
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,
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16、解:以
D為原點,
DA、
DC、
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所在的直線分別為
x、
y、
z軸,
建立空間直角坐標(biāo)系,設(shè)正方體
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棱長為
a,則
D(0,0,0),
A(
a,0,0),
B(
a,
a,0),
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(0,0,
a),
E(
a,
a,
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),
F(
a,
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,0),
G(
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,
a,0).
(1)
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,
a,
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),∴
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.
∴
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∵
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,∴
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平面
AEG.
(2)由

,
a,
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),
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=(
a,
a,
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)
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科目:高中數(shù)學(xué)
來源:不詳
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在正方體

中,若點

(異于點
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)是棱上一點,則滿足
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與
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所成的角為

的點
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的個數(shù)為
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(本小題滿分12分)如圖,在多面體
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中,
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平面
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,
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,且
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是邊長為2的等邊三角形,
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與平面

所成角的正弦值為

.
(Ⅰ)在線段
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上存在一點F,使得
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面
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,試確定F的位置;
(Ⅱ)求二面角

的平面角的余弦值.

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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(本小題滿分12分)已知直三棱柱
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中,
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,

,點

在
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上.
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(1)若
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是
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中點,求證:

∥平面

;
(2)當(dāng)
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時,求二面角

的余弦值.
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如圖所示,在棱長為2的正方體
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中,

、

分別為
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、

的中點.
(Ⅰ)求證:

//平面

;
(Ⅱ)求證:

;

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科目:高中數(shù)學(xué)
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(本小題滿分14分)如圖,在四棱錐

中,
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面
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,四邊形

是正方形,

是

的中點,

是

的中點

(1)求證:

面

;
(2)求證:

面

.
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(本題滿分14分)如圖2,正方體

中,
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分別是棱
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的中點.
(1)求證:直線

∥平面

;
(2)求證:平面

∥平面

.

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科目:高中數(shù)學(xué)
來源:不詳
題型:解答題
(1)證明直線和平面垂直的判定定理,即已知:如圖1,

且

,

求證:

(2)請用直線和平面垂直的判定定理證明:如果一條直線垂直于兩個平行平面中的一個,那么它也垂直于另一個平面,即
已知:如圖2,

求證:
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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
兩條異面直
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線在同一個平面內(nèi)
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的射影一定是( )
A.兩條相交直 線 | B.兩條平行直線 | C.兩條垂直直線 | D.以上均有可能 |
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