.(本小題滿分12分)
如圖5所示的多面體是由底面為
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的長方體被截面
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所截
而得到的,其中
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.
(1)求
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;
(2)求點
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到平面

的距離.
解:(1)以
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為原點,
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所在直線為
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軸,
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軸,
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軸建立空間直角坐標系
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,
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,
設

.
由
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,得
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,
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.
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.
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.
(2)設
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為平面

的法向量,
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,由
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得
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
又

,設

與
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的夾角為

,
則

.

到平面

的距離
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
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
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
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
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
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
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
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