西南大学22年9月1245 几何学在线作业
1245 几何学1.[单选题] 两点(4,1,2)和(-2,2,1)确定直线的线坐标是( )
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A.
B.
C.
D.[-1,3,5]
2.[单选题] 设三向量a,b,c不共面，那么当<img width="75" height="23" class="kfformula" style="width: 75px; height: 23px;" src="data:image/png;base64,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" data-latex="\lambda a+\mu b+\nu c"/>和b,c共面时，<img width="53" height="21" class="kfformula" style="width: 53px; height: 21px;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFQAAAArCAYAAADmH6/VAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAEgSURBVGhD7di9TQNBFEXhBUqgAxqgAQpARAQEdAByAUSktIBEBRCSIEEN9EAFCCEROYJ7dmcT5B8Zr7zycD7pambHifU0b2btRpIkSZIkaYnz5CO5aZ80iKvkO7GoAzlIKCg7VQN5TSjqUftUib0yjuErOUumyRMLWs9+YtsP7CGhqNz8Vdgt41gey3haxq23U8ax0Pbv3XThd+Hiuu6mK3tLJt20frQ6LV9V24+FAvLqdJFQUM5T/VH/87N/B2VOUTkCtKK+zU/ap85twhq7datt+lKimPfJZXLHQkFxebl/SY5Z+GWdS+kzqfJ8pmjsQnbjrNbu257f+VriMKFgz8m8c5J/nqpo+03gBudGX7T7+IyiE0mSJEmSJOnfa5of3wkxO99zeBwAAAAASUVORK5CYII=" data-latex="\lambda ="/>( )
A.2
B.-1
C.1
D.0
3.[单选题] 两直线<img width="89" height="30" class="kfformula" style="width: 89px; height: 30px;" src="data:image/png;base64,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" data-latex="{x}_{1}-2{x}_{2}=0"/>和<img width="129" height="25" class="kfformula" style="width: 129px; height: 25px;" src="data:image/png;base64,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" data-latex="4{x}_{1}-5{x}_{2}+{x}_{3}=0"/>的交点坐标是( )
A.(2,1,3)
B.(2,-1,-3)
C.(-2,-1,3)
D.(2,-1,3)
4.[单选题] 已知向量a=(1,2,1),b=(2,1,3),那么3a-2b=( )
A.(-1,-4,-3)
B.(1,4,3)
C.(1,4,-3)
D.(-1,4,-3)
5.[单选题] 下列概念是射影几何讨论对象的是( )
A.线段中点
B.平行
C.调和点列
D.角平分线
6.[单选题] 直线x+y-z+1=0,x+y=0和直线x-2y+3z-6=0,2x-y+3z-6=0的距离是( )
A.C.2
B.5
C.1
D.0
7.[单选题] 通过点(1,2,-1)和z轴的平面方程( )
A.B.2x-y=0
B.x+y=0
C.x-y=0
D.2x+y=0
8.[单选题] 已知向量a=(5,-2,1),b=(4,0,6),那么<img width="58" height="25" class="kfformula" style="width: 58px; height: 25px;" src="data:image/png;base64,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" data-latex="a\times b="/>( )
A.(-12,26,8)
B.(12,26,8)
C.(-12,-26,8)
D.(12,-26,-8)
9.[单选题] 设点C分线段AB为5:2,A点坐标(3,7,4),C点坐标(8,2,3),则B点坐标是( )
A.(10,2,7/5)
B.(10,0,13/5)
C.(1/2,0,12/5)
D.(1,0,5)
10.[单选题] 曲面<img width="99" height="22" class="kfformula" style="width: 99px; height: 22px;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMsAAAAuCAYAAACGcu0CAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAASCSURBVHhe7Zy7qhRBFEVHcxE0NdJUEUQwEQNBBb9AjAQFwczERIxERcRE1MzcRExFwcjMBxgZqBcDUxX8AT1rus6lKKbn9vSzunsv2PRjnNtVdeo8qmbGhRBCCCGEEEIIIYQQQgghhBBCCCGEEEKIybErHHNmv+m26YfptGnLdM00JS6YjhSni7Om66Z3y6v8mIM9Rstz09HidMkrE/emwknT0+J0Cdf/THGfc2Lq9hgtB03vi9NtzpuYTES4KYCj0KcY+nynOM2KOdijlN3hmCt7TMdNlCnO33A8EI5jZ5/pUXG6zS/ToeI0K+Zgj0lx1fTN1Gcku2HiuWQByg6uu3z+bxPPGwND2IMMhy1yzL7ZgEEwTJ8TCaOwjnBoA6VIVxNkiMlXl77tQaDCHojST86yhr6jCeXGqongi/C2F7YsnHHEXBf3KUNGdznLGih9mgwOUSldSO8E7yHlr4KI2ubC1jPWWBylqT2a0ruz5L7Ad4jwe003l1dFZO+jTDln+m5a5TA4C5wIxybQlyemK6bP3DA2dew+GcoegzKEszCoRAREJPWdFb9HNI93WzAEH9i5YeBiOHbNB9MfE7tAZfhukEP/KE+IvDhUmil4nfItdgY+5LtnckfhPYeL016h5GRzAcXtxk7uDEPaY1Yw4DgDAw6+R8/k8R0mDOPlDREdw3Edi3ubUqcMWwdtWLUQx1G8fzwTxRAI6AP9BQJE2j/U5yYGMDb0ifZwRPSNdnpb27RHU3gubZ0sDHqcNYhedNonnRuDCZdOwqa06SzphHdovy/6OeffpM5C37jvDpULtNPbxNh7lkd1bUFf/W9sqp3GZ/LOwiDEA++ZhUHtGp7dhrPQ/jKHJhu4kXEk+pZmCAKDR+2cSCcn7cPxcfocmbyzpNBZOh1nm65oy1mYQFUyH05B3+LJxnu4R1tyhnZWie5DMjtn8fVJW9ErLh1SEc153qrXUJWJwd+v4iheXnpJ5ngmTcu3qvj766jqGghb0MdcM4pDn2bjLB5lmcB9gEM0ySxkvyqOAmUlmGfSXCM2Ts445e4o0LuzDPk5y5lwfB2ODhMy3rbMARzllOmWiS85Otxf1VZ+5wFvwtHhtypsRX9ZXuUF/bhv4rcp/EbFwbHrOg+2jLP3JmqjZB4tvoPk6xMGMr4GojalS5XovSl1DcAkKssoZW3lWfQtfo0Jxz1ey42yjEL7489YcmLSmeWSiaj604RxMAyfjhOxAYPwKfZjUxy9h4R2vjDR7ssmyqtYZV+jfxmO8dfW74bj23DMBcadPn40ERQQfWMifjU9NOVij9nAxCNKYQjfkuQeu0bcw0hd1vJ1MgubAkSwMq1bbzHZvL/0zbNNbuuVNKPQVtqJXeKsnwO0h/H0sUSMM/fSrCgaUMdZ2oTJh3IsaUQFxvJFyjagzEi/x9UFHpnjSEdEpGR7YFJJI0QAR6H8cmchk5BRyGzKKkJExI4CZJr0nhghY/h/w8YGmxZ8XsGu1zHTJ9Mzk8ovIYQQQgghhBBCCCGEEEIIIYQQZSwW/wH8ZzqxCdsT1wAAAABJRU5ErkJggg==" data-latex="{x}^{2}+2{y}^{2}-{z}^{2}=1"/>的对称中心坐标是( )
A.(1,2,-1)
B.(0,0,0)
C.(2,1,1)
D.(1,2,1)
11.[单选题] 点C为线段AB的中点，则单比(ABC)=( )
A.0
B.2
C.1
D.-1
12.[单选题] 下列命题叙述正确的是( )
A.射影对应是透视对应
B.中心对应是射影对应
C.透视仿射对应是透视对应
D.仿射对应是射影对应
13.[单选题] 已知四面体的顶点A(1,2,0),B(-1,3,4),C(-1,-2,-3),D(0,-1,3),它的体积是( )
A.57/7
B.59/6
C.53/6
D.51/7
14.[单选题] 设空间圆的方程<img width="81" height="25" class="kfformula" style="width: 81px; height: 25px;" src="data:image/png;base64,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" data-latex="{x}^{2}+{y}^{2}+{z}^{2}=4"/>,x+y+z=3,那么圆的半径等于( )
A.2
B.8
C.3
D.1
15.[单选题] 下列命题叙述正确的是( )
A.A.中心射影的基本性质是保结合性
B.中心射影是一维射影变换
C.直线间的透视仿射对应是中心射影
D.中心射影把无穷远直线变成无穷远直线
16.[单选题] 向量a=(3,2,1)和b=(2,-3,0)的位置关系是( )
A.平行
B.相交不垂直
C.垂直
D.重合
17.[单选题] 下列量是射影不变量的是( )
A.面积比
B.二线段之比
C.交比
D.单比
18.[单选题] 关于二次曲线的命题叙述不正确的是( )
A.D.二次曲线不可能以无穷远直线作为直径
B.二次曲线分有心和无心两种
C.抛物线存在共轭直径
D.双曲线有两条渐近线
19.[单选题] 已知x轴上的射影变换式为<img width="63" height="25" class="kfformula" style="width: 63px; height: 25px;" src="data:image/png;base64,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" data-latex="{x}^{'}=\frac {2x-1} {x+3}"/>,那么无穷远点的对应点是( )
A.2
B.-1/3
C.0
D.2/3
20.[单选题] 三角形的顶点A,B,C的坐标分别是(2,4,3),(11,3,8),(5,11,12),那么BC的长度是( )
A.根号29
B.2倍的根号29
C.3倍的根号19 南开大学答案q7 6 1 2 9 6 0 2 1
D.根号19
21.[单选题] 已知A,B,C三点的坐标分别是(2,4,3),(4,1,9),(5,11,12),联结这三点构成三角形，则三角形是( )
A.直角三角形
B.锐角三角形
C.钝角三角形
D.等腰三角形
22.[单选题] 关于极点与极线的性质叙述不正确的是( )
A.共点线的极点必共线
B.点关于二次曲线的极线有多条
C.二次曲线是自共轭点的轨迹
D.共线点的极线必共点
23.[单选题] 若交比(AB,CD)=2,则(AD,CB)=( )
A.-1
B.2
C.-2
D.1
24.[单选题] 对于平行四边形ABCD，D在仿射标架中的坐标是( )
A.(-1/2,1/2)
B.(1/2,1/2)
C.(1/2,-1/2)
D.(-1/2,-1/2)
25.[判断题] 一个实数与向量相乘所得向量与原向量方向同向
A.正确
B.错误
26.[判断题] 向量的大小不能为0
A.正确
B.错误
27.[判断题] 两直线间的透视对应不具有传递性
A.正确
B.错误
28.[判断题] 二维射影坐标系下，射影点与三元数组构成一一对应关系
A.正确
B.错误
29.[判断题] 数乘向量不可能是零向量
A.正确
B.错误
30.[判断题] 两向量外积是一个非零向量
A.正确
B.错误
31.[判断题] 两条平行直线不属于柱面
A.正确
B.错误
32.[判断题] 二线段之比在仿射变换下保持不变
A.正确
B.错误
33.[判断题] 仿射对应和仿射变换的仿射性质不同
A.正确
B.错误
34.[判断题] 数乘向量的方向不确定
A.正确
B.错误
35.[判断题] 两向量一定共面
A.正确
B.错误
36.[判断题] 一维基本型只有点列和线束
A.正确
B.错误
37.[判断题] 二次曲线的中心不是仿射不变图形
A.正确
B.错误
38.[判断题] 德萨格定理的对偶命题是其逆命题
A.正确
B.错误
39.[判断题] 射影对应具有传递性
A.正确
B.错误
40.[判断题] 一个向量不可能是线性组合
A.正确
B.错误
41.[判断题] 两平面间的中心射影是两平面间的透视对应
A.正确
B.错误
42.[判断题] 旋转曲面不是直纹面
A.正确
B.错误
43.[判断题] 椭圆抛物面关于原点对称
A.正确
B.错误
44.[判断题] 向量a+b与a-b可以构成平行四边形
A.正确
B.错误
45.[判断题] 单叶双曲面的同族上的任意两直母线必异面
A.正确
B.错误
46.[判断题] 双曲抛物面的同族的任意两直母线异面
A.正确
B.错误
47.[判断题] 射影平面上没有无穷远直线
A.正确
B.错误
48.[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
49.[判断题] 三点可以唯一确定一平面
A.正确
B.错误
50.[判断题] 交比是正交变换的不变量
A.正确
B.错误
51.[判断题] 二次曲线的奇异点的个数可以是无穷多
A.正确
B.错误
52.[判断题] 有一个向量是零向量的一组向量必然线性相关
A.正确
B.错误
53.[判断题] 退化的二次曲线有无穷多奇异点
A.正确
B.错误
54.[判断题] 三向量的混合积等于以这三向量为邻边的平行六面体的体积
A.正确
B.错误
55.[判断题] 直线与平面所成的角不能为钝角
A.正确
B.错误
56.[主观填空题] 过原点且斜率为2的直线的线坐标是_________
A.
57.[主观填空题] 由两对对应元素确定的对合方程是________
A.
58.[主观填空题] 双曲线x=0绕z轴旋转，得到旋转曲面的方程是_______
A.
59.[主观填空题] i,j,k是两两垂直的单位向量，那么_____
A.
60.[主观填空题] 无穷远直线的线坐标是_____
A.
61.[主观填空题] 在直角坐标系，向量a=+b-c)\times (a-b+c)="/>_______
A.
62.[主观填空题] 向量a=i+j和b=i+k的夹角是________
A.
63.[主观填空题] 射影对应使得参数为 0,2,-1分别对应1,-3,0的参数表达式________
A.
64.[主观填空题] 直线x-3=0关于二阶曲线的极点是_______
A.
65.[主观填空题] 已知A,B,C的齐次坐标分别是(1,2,5),(1,0,3),(-1,2,-1),且(AB,CD)=5,那么D点的坐标是______
A.
66.[主观填空题] 直线{-1}"/>与平面x-2y+4z-1=0所成角的余弦是__________
A.
67.[主观填空题] 点(1,2,0)的齐次坐标方程是__________
A.
68.[主观填空题] 已知向量a=(0,1,1),b=(1,0,1),c=(1,1,0),则混合积(abc)=_______
A.
69.[主观填空题] 已知平行四边形ABCD中顶点A,B,C的坐标分别为(1,0,2),(0,3,-1),(2,-1,3),那么点D的坐标是________
A.
70.[主观填空题] 已知向量a=(3,5,7),b=(0,4,3),c=(-1,2,-4),设u=3a+4b-c,v=2b+c,_______
A.
71.[主观填空题] 点(-1,-3,5)到直线的距离是______
A.
72.[主观填空题] 经过原点(0,0,0),且与向量(1,1,0),(1,0,1)平行的平面方程________
A.
73.[主观填空题] 已知一个四面体的顶点A,B,C,D的坐标分别是(1,2,0),(-1,3,4),(-1,-2,-3),(0,-1,3),它的体积是_____
A.
74.[主观填空题] 已知A(1,1,1),B(1,-1,1),D(1,0,1)为共线三点，且(AB,CD)=2,那么C的坐标是________
A.
75.[主观填空题] 椭球面长半轴顶点坐标是_______
A.
76.[主观填空题] 设三向量a,b,c两两垂直，并且<
A.
77.[主观填空题] 已知平行四边形ABCD中顶点A,B,C的坐标分别为(1,0,2),(0,3,-1),(2,-1,3)，则对角线交点的坐标是______
A.
78.[主观填空题] 直线
A.
81.[问答题] 以A(1,0,0),B(0,1,0),C(0,0,1)为顶点的三点形为坐标三点形，写出坐标三点形的三边方程
A.
82.[问答题] 求顶点m(1,2,4)，轴与平面2x+2y+z=0垂直,且经过点N(3,2,1)的圆锥面方程
A.
83.[问答题] 求射影变换width="98" height="30" style="width: 98px; height: 30px;"/>的不变点
A.
84.[问答题] 求双曲线渐近线方程
A.
85.[问答题] 求单叶双曲面的经过点(2,3,-4)的直母线
A.
86.[问答题] 求两直线iVBO极线
A.
87.[问答题] 设向量a=(1,5,2),b=(0,-3,4),c=(-2,3,-1),求-3a+2b+4c
A.
88.[问答题] 设在直角坐标系中,平面<相交，求二平面所成二面角的角分面的方程
A.
89.[问答题] 求经过两平面4x-y+3z-1=0和x+5y-z+2=0的交线，且经过点(1,1,1)的平面方程
A.
90.[问答题] 设有一个固定平面和垂直于它的一条定直线，求到定平面与到定直线的距离相等的点的轨迹
A.
91.[问答题] 求射影变换式，使直线上以0,1为坐标的点和无穷远点顺次对应以-1,0,1为坐标的点
A.
92.[问答题] 设三点形ABC三边BC,CA,AB分别与二次曲线切于P,Q,R，QR与BC交于点X，求证:(BC,XP)=-1
A.
93.[问答题] 证明两直线共面
A.
94.[问答题] 证明方程表示的曲面是柱面
A.
95.[问答题] 证明方程(x+y)(y+z)=x+2y+z所表示的曲面是柱面
A.
96.[问答题] 已知射影对应(A,B,C,P,Q,R)<img width="36" height="20" class="kfformula" style="width: 36px; height: 20px;" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEwAAAArCAYAAADSZm7JAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAACbSURBVGhD7daxDcIwEAVQS4xAQc8CLIBEzwRswCSswAwUbJIVmIEV4C5OSmQXSIjoPenL53Q5n+IUAAAAAIAl2EVutaTXK7Kv5W+spvVfbCKHyH3c0bSN5JQdxx1dTpFsWn7T6DQ3LddFm1/0mxkiNFwij0gewDof8Nk1klOVFwANeTvmZGlWp2zWuZa05G/EM2K6AAAAACalvAEILiPgHTGLOAAAAABJRU5ErkJggg==" data-latex="\to "/>(B,C,A,Q,R,X),证明:X与P重合
A.
97.[问答题] 已知两直线证明此二直线相交
A.
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