《 1245》20秋西南大学在线作业答案答案
12451.[单选题] 下列关于直纹面说法不正确的是( )
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A.柱面是直纹面
B.双曲抛物面是直纹面
C.平面是直纹面
D.椭圆抛物面是直纹面
2.[单选题] 下列命题叙述正确的是( )
A.三向量的混合积是大于0的数
B.两向量的内积是向量
C.三向量的混合积是向量
D.两向量的外积是向量
3.[单选题] 不属于仿射几何几何研究的对象是( )
A.面积之比
B.交比
C.二平行线段之比
D.距离
4.[单选题] 直线2x+3y+z-1=0,x+2y-z+2=0与xoz平面的交点是( )
A.(-1/3,0,5/3)
B.(-1/3,0,-5/3)
C.(-1/3,0,5/3)
D.(1/3,0,5/3)
5.[单选题] 已知a( )
A.(1,1,1)
B.(1,-1,1)
C.(-1,1,1)
D.(1,-1,-1)
6.[单选题] 射影平面上两直线的距离是()
A.-1
B.无法确定
C.0
D.1
7.[多选题] 下列命题叙述正确的是( )
A.抛物线无共轭直径
B.抛物线是有心二次曲线
C.抛物线的直径是相互平行的
D.抛物线是无心二次曲线
8.[多选题] 关于点列和线束的命题叙述错误的是( )
A.两不同线束之间的透视对应是一一对应
B.透视对应是射影对应
C.点列和线束之间不能建立射影对应
D.两不同点列之间透视对应就是两直线间的中心射影
9.[多选题] 三向量共面的充要条件是( )
A.三向量线性相关
B.三向量混合积是零
C.有一个向量是零向量
D.一向量是另外两向量的线性组合
10.[多选题] 下列关于二次曲线性质叙述正确的是( )
A.无穷远点关于二次曲线的极线是二次曲线的直径
B.二次曲线的中心的极线是无穷远直线
C.渐进线是直径，其共轭直径就是它本身
D.彼此平分与对方平行弦的两直径是一对共轭直径
11.[多选题] 两向量共线的充要条件是( )
A.有一向量是零向量
B.两向量的外积是零向量
C.两向量线性相关
D.两向量线性无关
12.[多选题] 下列二次曲面属于直纹面的是（ ）
A.椭球面
B.双叶双曲面
C.单叶双曲面
D.双曲抛物面
13.[判断题] 二次曲线的直径是通过中心的有穷远直线
A.正确
B.错误
14.[判断题] 平行四边形的仿射不变图形是平行四边形
A.正确
B.错误
15.[判断题] 二次曲线的中心不可能是无穷远点
A.正确
B.错误
16.[判断题] 两向量外积是一个非零向量
A.正确
B.错误
17.[判断题] 球坐标系建立了空间所有点和所有三元数组之间的一一对应
A.正确
B.错误
18.[判断题] 平面方程不需要三个变元全出现
A.正确
B.错误
19.[判断题] 无穷远点有非齐次坐标
A.正确
B.错误
20.[判断题] 二次锥面是旋转曲面
A.正确
B.错误
21.[判断题] 三点形的对偶图形就是它自己
A.正确
B.错误
22.[判断题] 射影点没有点方程
A.正确
B.错误
23.[判断题] 柱面不是二次曲面
A.正确
B.错误
24.[判断题] 射影对应具有传递性
A.正确
B.错误
25.[判断题] 平面既是柱面又是锥面
A.正确
B.错误
26.[判断题] 两相交向量可唯一确定空间一平面
A.正确
B.错误
27.[判断题] 线性无关的向量不共线
A.正确
B.错误
28.[判断题] 两向量的内积是一个数，两向量的外积是一个向量
A.正确
B.错误
29.[判断题] 混合积等于3向量为棱边的平行六面体的体积
A.正确
B.错误
30.[判断题] 若两平面平行，则它们的法向量平行
A.正确
B.错误
31.[判断题] 向量a+b与向量a-b不可能平行
A.正确
B.错误
32.[判断题] 共线向量一定是共面向量
A.正确
B.错误
33.[判断题] 射影平面可使中心射影一一对应
A.正确
B.错误
34.[判断题] 外积满足交换律
A.正确
B.错误
35.[主观填空题] 向量a=(1,1,0),b=(1,0,1)的夹角是_______
A.
36.[主观填空题] 二阶曲线<img width="143" height="23" class="kfformula" style="width: 143px; height: 23px;" src="data:image/png;base64,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" data-latex="{x}^{2}_{1}-2{x}^{2}_{2}+3{x}^{2}_{3}-{x}_{1}{x}_{3}=0"/>过点<img width="50" height="25" class="kfformula" style="width: 50px; height: 25px;" src="data:image/png;base64,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" data-latex="(2,\sqrt {\frac {5} {2}},1)"/>的切线方程是 ______________
A.
37.[主观填空题] 无穷远直线的线坐标是_____
A.
38.[主观填空题] 通过点(3,2,-4),且在x轴与z轴上的截距分别为-2，-3，那么平面方程为_________
A.
39.[主观填空题] 在直角坐标系，向量a=(1,0,1),b=(1,-2,0),c=(-1,2,1),则<img width="133" height="25" class="kfformula" style="width: 133px; height: 25px;" src="data:image/png;base64,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" data-latex="(3a+b-c)\times (a-b+c)="/>_______
A.
40.[主观填空题] 52.设A,B,C,D四点共线，单比(ABC)=2,(ABD)=-1,则交比(AB,CD0=______;(AD,CB)=_______
A.
41.[主观填空题] 两个射影点列成透视对应的充要条件是___________
A.
42.[主观填空题] 通过原点与点(6,-3,2)且和平面4x-y+2z=0垂直的平面方程是________
A.
43.[主观填空题] 曲面<img width="117" height="23" class="kfformula" style="width: 117px; height: 23px;" src="data:image/png;base64,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" data-latex="{x}^{2}+2{y}^{2}-{z}^{2}=1"/>与y-z=0的交线在xoy面上的射影曲线为_________
A.
44.[主观填空题] 16.已知向量a=(1,0,-1),b=(2,3,0),c=(0,2,3),则有这3个向量张成的平行六面体的体积是________
A.
45.[主观填空题] 已知向量a=(1,1,0),b=(2,03),则<img class="kfformula" src="data:image/png;base64,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" data-latex="a\times b=" width="76" height="27" style="width: 76px; height: 27px;"/>________
A.
46.[主观填空题] 直线<img class="kfformula" src="data:image/png;base64,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" data-latex="\frac {x} {-1}=\frac {y-1} {1}=\frac {z-1} {2}" width="106" height="30" style="width: 106px; height: 30px;"/>与平面2x+y-z-3=0的交点坐标是___________
A.
47.[主观填空题] 直线上参数分别为1，0，<img width="23" height="14" class="kfformula" style="width: 23px; height: 14px;" src="data:image/png;base64,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" data-latex="\infty "/>的三点分别对应0，<img width="29" height="19" class="kfformula" style="width: 29px; height: 19px;" src="data:image/png;base64,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" data-latex="\infty "/>，1的三点的射影变换参数表示是_________________
A.
48.[主观填空题] 设a,b是不共线的向量，那么<img class="kfformula" src="data:image/png;base64,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" data-latex="\left | {a+b} \right |=\left | {a-b} \right |" width="107" height="26" style="width: 107px; height: 26px;"/>的充要条件是________
A.
49.[主观填空题] 已知向量a=(-1,2,1),b=(0,1,1),那么a与b的夹角是_________
A.
50.[主观填空题] 点P(3,4,5）绕Oz轴旋转生成的圆的方程_____________
A.
51.[问答题] 已知二次曲线<img width="156" height="18" class="kfformula" style="width: 156px; height: 18px;" src="data:image/png;base64,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" data-latex="{x}^{2}+2xy-3{y}^{2}+2x-4y=0"/>,(1)证明它是双曲线；(2)求中心坐标；(3)求与直线<img width="73" height="21" class="kfformula" style="width: 73px; height: 21px;" src="data:image/png;base64,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" data-latex="2x+y=0"/>平行的直径及其共轭直径的方程；(4)求渐近线方程
A.
52.[问答题] 22.已知两条直线m: <img width="70" height="21" class="kfformula" style="width: 70px; height: 21px;" src="data:image/png;base64,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" data-latex="\frac {x-2} {2}=\frac {y} {-1}=\frac {z-1} {0}"/>和n:<img width="68" height="23" class="kfformula" style="width: 68px; height: 23px;" src="data:image/png;base64,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" data-latex="\frac {x-1} {2}=\frac {y-1} {2}=\frac {z+1} {0}"/>,证明m和n是异面直线。
A.
53.[问答题] 求通过点P(-5,0,1)的二阶曲线<img class="kfformula" src="data:image/png;base64,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>的切线方程
A.
54.[问答题] 34.已知双曲抛物面{9}=2z"/>,过点(4,3,0）两条直母线方程。
A.
55.[问答题] 给定方程i的各种实数值时，它表示怎样的曲面?
A.
56.[问答题] 说明方程<img width="84" height="31" class="kfformula" style="width: 84px; height: 31px;" src="data:image/png;base64,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" data-latex="z=\frac {1} {{x}^{2}+{y}^{2}}"/>表示旋转曲面，并说明它是怎样产生的
A.
57.[问答题] 求射影变换k+ov38al/N6geORLXNla3zbWgtWDluTM2OyfSXuXdxACt8WHAcSCkM4mGmM2gyo15yNIKzzPyWzMCSCZKSR5Mu99SWqMGYBlfp7M7G/1Dm+MmQEfIeKHF2zsHzoYY4wxxhhjjDHGGGOMMcYYY4wxxhhjjDHGGGOMMcYYY24vNzf/AamXwFhO3Y7QAAAAAElFTkSuQmCC" data-latex="\rho {x}^{'}_{2}=2{x}_{1}+{x}_{2}+2{x}_{3}"/>,<img width="145" height="24" class="kfformula" style="width: 145px; height: 24px;" src="data:image/png;base64,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" data-latex="\rho {x}^{'}_{3}=2{x}_{1}+2{x}_{2}+{x}_{3}"/>的不变元素
A.
58.[问答题] 已知圆锥面的顶点是原点,对称轴的方程是<img width="91" height="25" class="kfformula" style="width: 91px; height: 25px;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIoAAAA1CAYAAACeG3PEAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAANjSURBVHhe7ZvNq05RFMZf/gFkLjESRfIxIDEgyYAy8DE0UJIJKWWGiZgYKEaSgYGbiYSBJElIFDFA8jH0lT+A53fOXjm9da/73nvP3qf3fX71tPc+N1nnnLXWXnvv8/aMMcYYY4wxxhhjjDHGGGOMMcYYY4yZQWalNie7pQXSQumBtEEKDqY2N/Ol/dJK6bl0RoJjqY1xKbZJV+tub5W0Wfos3eLCMLJIulZ3q5v/k9oL0m2pFKel9RJ2vONC4rvE30rDs+HZhY1dsKlVyCbcLBCtzZdSEmwhq+C4kUWWS+HIXQGbCDRsHRmeSkRHV8CJySC8DDggMSaSuwB2hUOPDBG9Ea1kmdKRS6TivAHjktNhk3CSILvzzk5tDrg5IpTIpRiDr6ndK72tu0V5n1oceYt0rxqVBScZk65Xozqojtbd4YSHT01CIUZ00DL10O9CHcALIaPgyNhFxot6qhRR/PPswibGXZkORx7qE5x6pOoB83/IaM3CNTKLSZTYcJsKpN2ppttT0sO6Oy5MMYekK9Iy6ZU0yGYW//5E3R2YD1KpjcZJk8NR5iYNwsfUtgE7wtPlZ1IbTOV5tWlPRQ5HWZE0CJdT2wY7pEFfRD8vktoAR95YdycNgXW/7hozglBvsCxmudel3VkzDiWLWZyFDa49EnsDEzGdYva81PYp63SKWWoLr7AmoP9sxXSYnFv4/fAdCo7yshqZTlPSUThLuVt3TdcpVaMMUp+0BdvzJ6XV0jmJr+4+SWQ6lpv0ufZL2intk75JOWF6xh6C6rDEZiB2HZG2SrntyU5smZesTzjPwQ4+JeBcJ2yJ1Rh/D/rHucA2CuX+1WF2e0pNPetSW7I+IVPwacMa6ZIUtsyRyHYXq9E/B3qd2lyQddl4XCr9kM5KEKu/3PYUgUO3UlNOE5yA6Gx+TtD/5R2RS/YrdZLMc2p+UBXZeOhPtrnBSJ3cdPMl5abfCcK25r4G01Ls42BvbrCv+XUbtmS3p8TUsyS1j6Xt0u9qVIZN0hMpisK1Emn+TTWqM85i6aa0iwuZ4f+fJz2qRjU4MdNkVntKOApH/nek4xIvpWSdwm9kbtTdClYV1Cdh0xfpmcR1yP07GoIKe8JxgS0FHByG9nc9xhhjjDHGGGOMMcYYY4wxZqbo9f4CLi+g8AFe5H0AAAAASUVORK5CYII=" data-latex="\frac {x} {l}=\frac {y} {m}=\frac {z} {n}"/>,轴线与母线的夹角为<img width="25" height="21" class="kfformula" style="width: 25px; height: 21px;" src="data:image/png;base64,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" data-latex="\theta "/>，求证:<img width="222" height="30" class="kfformula" style="width: 222px; height: 30px;" src="data:image/png;base64,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" data-latex="{\cos {\theta }}^{2}=\frac {{(lx+my+nz)}^{2}} {({x}^{2}+{y}^{2}+{z}^{2})({l}^{2}+{m}^{2}+{n}^{2})}"/>
A.
59.[问答题] 如果3向量a,b,c不共面，那么<img class="kfformula" src="data:image/png;base64,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" data-latex="a\times b" width="61" height="29" style="width: 61px; height: 29px;"/>,<img class="kfformula" src="data:image/png;base64,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" data-latex="b\times c" width="61" height="28" style="width: 61px; height: 28px;"/>,<img class="kfformula" src="data:image/png;base64,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" data-latex="c\times a" width="64" height="30" style="width: 64px; height: 30px;"/>也不共面
A.
60.[问答题] 设三点形ABC的边AB,BC,CA绕同一直线上三点P,Q,R旋转，顶点B,C在两条定直线上，求证:顶点A也在一条定直线上
A.
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