已知正三棱柱ABC-A1B1C的各条棱长都为a,P为A1B上的点,且PC⊥AB(1)求...
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发布时间：2024-02-14 20:03
共1个回答
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时间：2024-03-12 08:14
连接MC，则MC为PC在平面ABC上的射影．
∵PC⊥AB，∴MC⊥AB，∴M为AB中点，
又PM∥AA1，所以P为A1B的中点．
过M作MN⊥AC于N，连接PN，则PN⊥AC，∴∠PNM为二面角P-AC-B的平面角
在Rt△PMN中，由|PM|=a2，|MN|＝34a，得tan∠PNM＝|PM||MN|＝233．
所以二面角P-AC-B的正切值为233…（6分）
（Ⅱ）∵M是AB中点，∴B到平面PAC距离等于M到平面PAC距离的2倍，
又由（I）知AC⊥平面PMN，∴平面PMN⊥平面PAC，
过M作MQ⊥PN于Q，则MQ⊥平面PAC，|MQ|＝|PM|?|MN||PM|2+|MN|2＝a2×34a已赞过已踩过你对这个回答的评价是？评论收起 // 高质or满意or特型or推荐答案打点时间 window.iPerformance && window.iPerformance.mark('c_best', +new Date); 推荐律师服务：若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询 ._1uevpeq{zoom:1;background-color:#fff;border:0;margin-bottom:10px;padding:30px 0 20px 42px;position:relative}._1uevpeq.ec-1841{padding:20px 0}._1uevpeq.ec-2246{padding:20px 0 10px}.ec-1841 .y7we4hu{font-size:16px;margin-bottom:-5px}.y7we4hu{color:#7a8f9a;height:25px;line-height:25px;overflow:hidden;position:relative}.y7we4hu h2{margin:0;padding:0}.y7we4hu:after{clear:both;content:" ";display:block;height:0;visibility:hidden}a.tycfu7u{color:#666;float:right;font-size:12px;margin-left:8px;text-decoration:none}.hhhv6ex{color:#666;font-size:13px;line-height:normal;line-height:20px;margin-top:10px}.vnsdjzp{margin-top:15px;position:relative}.vnsdjzp h3{font-weight:400;padding:0}.vnsdjzp a{text-decoration:none}.vnsdjzp em{color:#d81419;font-style:normal}.ec-2246 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