2022 英语周报 八年级 牛津HNX 3答案

19.【考查目标】必备知识:本题主要考查直三棱柱中的线线垂直、二面角的正弦值、空间向量等知识.关键能力:通过线线垂直的证明和二面角的求解考查了空间想象能力、逻辑思维能力和运算求解能力学科素养:理性思维、数学探索【解题思路】(1)先证明BA⊥BC,再利用AB,BC,BB1两两垂直建立空间直角坐标系,求出相关点的坐标,利用向量证明;(2)分别求出面BB1C1C和面DEF的一个法向量,通过求出两法向量夹角的余弦值的最大值来解决解:(1)因为E,F分别是AC和C1的中点,且AB=BC=2所以CF=1,BF=√5.如图,连接AF,由BF⊥A1B1,AB∥AB,得BF⊥AB,于是AF=BF+ABF=3,所以AC=√AF-CF=2.由AB2+BC2=AC2,得BA⊥BC,故以B为坐标原点,以AB,BC,B1所在直线分别为x,y,z轴建立空间直角坐标系B-xy则B(0,0,0),E(1,1,0),F(0,2,1),BF=(0,2,1)设B1D=m(0≤m≤2),则D(m,0,2),于是DE=(1-m,1,-2)所以B.DE=0,所以BF⊥DE(2)易知面BB1C1C的一个法向量为n1=(1,0,0)设面DFE的法向量为n2=(x,y,2),n,又靂=(1-m,1,-2),E=(-1,1,1)所以(1-m)x+y-2z=0-x+y+z=0,令x=3,得y=m+1,z=2-m,于是,面DFE的一个法向量为n2=(3,m+1,2-m),所以cos(n1,n2〉=)2设面BCC与面DFE所成的二面角为6,则in6=√1-m(n1,m2),故当m=时,面BBCC与面DFE所成的二面角的正弦值最小为,即当B1D=时,面BB1C1C与面DFE所成的二面角的正弦值最小.【解題关键】本题求解关键是建立恰当的空间直角坐标系,确定相关点的坐标,再利用空间向量进行运算

第二节读后续写( One possible version)Fliss immediately took the purse to the local police station with Molly. When they arrivedFliss tied Molly to a fireplug outside and went in herself. She handed the purse to a police officerand explained everything. Greatly touched, he shook her hand and thanked her for doing her duty,promising that he would do his best to find the owner Fliss felt reassured and went back withMolly. The next day, a journalist called to make an appointment for an interview.When the journalist came, they two were on the beach. The journalist was surprised to findthat Molly was picking up litter, following her master. Fliss told the journalist it was on the wayto collecting litter that Molly had found the purse. Hearing this, Molly stopped, wagging her tailas if she understood the whole situation. Having learned about the whole story, the journalist gotto know what they did to protect the local beach. Surprised and impressed, the journalist tooksome pictures. The next day they were on the front page of the newspaper. A minor action couldmake wonders!(162 words)

以上就是2022 英语周报 八年级 牛津HNX 3答案，更多英语周报答案请关注本网站。