12．如图.正四棱柱中..点在上且． (Ⅰ)证明:平面, (Ⅱ)求二面角的大小．解法一: 依题设..． (Ⅰ)连结交于点.则．由三垂线定理知.．··················——青夏教育精英家教网—

12．如图.正四棱柱中..点在上且． (Ⅰ)证明:平面, (Ⅱ)求二面角的大小．解法一: 依题设..． (Ⅰ)连结交于点.则．由三垂线定理知.．····················································································· 3分在平面内.连结交于点. 由于. 故.. 与互余．于是．与平面内两条相交直线都垂直. 所以平面．································································································ 6分 (Ⅱ)作.垂足为.连结．由三垂线定理知. 故是二面角的平面角．································································· 8分 . .． .．又.．．所以二面角的大小为．··························································· 12分解法二: 以为坐标原点.射线为轴的正半轴. 建立如图所示直角坐标系．依题设.． .．··································· 3分 (Ⅰ)因为.. 故.．又. 所以平面．································································································ 6分 (Ⅱ)设向量是平面的法向量.则 .．故.．令.则..．······························································· 9分等于二面角的平面角. ．所以二面角的大小为．·························································· 12分【查看更多】

题目列表(包括答案和解析)

如图，正四棱柱中，，点在上且．