第二节Then came the first class -- Chinese painting. The teacher showed us how to use a brush topaint bamboo on a piece of white paper. Then all the other students were in business. But it wasquite dificult for me. How could I hold the stiff brush and made it go as I wished? Hesitating for awhile, I tried dipping the brush into the ink bottle. When I took it out, drops of black ink fell onthe white paper. There was no bamboo, but big black dots!As I burnt with great embarrassment, Li Hua, who was next to me, gave me a warm smile. Ismiled back awkwardly She came over and demonstrated how to use the brush the brush movedacross the paper, and a lively bamboo appcarcd! With her help, I finally completed the task,although it was such a ugly one Aner that, we became good friends. She taught me Chinese whileI taught her English. We both made great progress in our studies. Yes, my mother was right. Asmile did make a difference

21.【解析】(1)连结B1C交BC1于E,连结ED因为D,E都是中点,所以DE∥AB1,………………2分又DEc平面BDC1,AB1￠平面BDC1,所以AB1∥平面BDC1,…………………………………………………………………4分(2)在直三棱柱ABC-A1B1C1中,AA1⊥平面ABC所以AA1⊥BD,AA1⊥AC,又BD⊥AC,所以AA1,AD,BD两两垂直5分以D为坐标原点建立如图空间直角坐标系设AB=AA1=2a(a>0)所以D(0,0,0),B(0,3a,0),C(0,0,-a),C1(2a,0,-a),所以BC=(2a,-3a,-a),CC=(2a,0,0),DC=(2a,0,-a)…………6分设平面BC1C的法向量为m=(x,y,z),m·BC=0由2ax=0所以x=0,令y=3,得z=-3,得m=(0,3,-3)分设平面BC1D的法向量为n=(x,y,z),n·BC=02ax-3ay-a=0,得Zar-az=o令x=1,得y=0,z=2,得n=(1,0,2)10分所以cos(m,n)=Im|n-万z×5--511分又由图易判断二面角C-BC1-D的平面角为锐角,所以其余弦值为√15…………………………………………………………………………………12分

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