下册习题7答案

(1)第I卦限 (2)第III卦限 (3)第VII卦限 (4)第VI卦限(a,b,0),(0,b,c),(a,0,c)点P至x,y,z轴和xOy,yOz,zOx面的距离分别为:b2+c2,a2+c2 ,|c|,|a|,|b|(a,-b,-c),(-a,b,-c),(-a,-b,c),(a,b,-c),(-a,b,c),(a,-b,c),(-a,-b,-c)( ,(1)3，1-22 (2)(1,-1,-4)，( ,33

，2(1,-1,-4)6(1)i-j+6k (2)-i+1j 2

3i-5j+2k3(1)不共线 (2)共线a=15,g=-151

421,,或1,,33 33r= (nr+mr)2m+

AO3

(AB+AC)(1)8, (2)-1,arccos-1 (3)0,π3 129,715.π3

(2)-1

5

,3(2,1,0) 5

,(,0, 28,28(1)(1,0,1) (2)(3,14,-9) (3)13i-10j-7k33

7,3,–10(1)k=-2 (2)k=-1,k=5(1)(26,4,-7) 2V=14,S=63,h=733(1)共面 (2)不共面(1)否 (2)否 (2)是(1)平行于z轴 (2)平行于yOz面 (3)过z轴 (4)过y轴(1)2(x-1)-(y+2)-5(z-3)=0

+=1 x+y+z-2=03x-6y+2z-49=07x-21y-9z=20y-3z=03x+2z-5=0y=2x+5y-z+16=015x+y+50z-167=02x+y+2z–233=0(1)在平面y=-2上(垂直于Oy轴 (2)平行于Ox轴(垂直于yOz面(3)过原点 (4)在xOy面上(1)x-1=y-2=z-3,x=1+2t,y=2-t,z=3+t x+1=y-2=z

x=-1+t,y=2,z=-3tx-2=y+3=z-8

x=2,y=t,z=8x-2=y+3=z-8,x=2+3s,y=-3-2s,z=8+5s x-1=y+3=z-2 x-1=y-2=z-3 x-1=y+3=z-2 x+1=y-2=z-1 - x-1=y-2=z-3

x-3=y-4=z+ z=

x=

y= (1)x=y-1=z-4 (2).x+5=y+8=z (1)814 (2) 7

x+2y-2z-1=–6(1)π (2)0,平行 (3)π,垂直 (4)arccos8 (1)异面 (2)相交于 (3)平行 (4)异面(1)0,平行 (2)π,垂直相交于3,-1,-1 2(3)0,直线在平面上

2arcsin1577,相交于(1,1,1) 7(1)4(x-3)-(y+2)+3(z+1)=0 (2) (3)(-5,2,4) (4)37,25, 7

x- y- z-

4717,(1,2,6), = =

,,

333z+2z-10,

-3=y-1x+y+z=

x+3y+3z=0,9x+8y-11z=(1)x+2y-2z-1=0 (2)2x-z+5=0 (3)x+2y-2z-1=(4)x+y+z=4 (5)y+z=0和y-z=0 (6)x+20y+7z-12=0(1)x-1=y-1=z+1 (2)x+1=y=z-4 (3)x-1=y-2=z-1 4x+4y+10z-63=0R (x+)+y+z= (1)旋转抛物面；(2)双曲抛物面；(3)(4)双曲抛物面；(5)单叶双曲面；(6)椭球面(4)x轴的平面；(5)圆心在(0,0,a的球面；(6)(7)椭球面；(8)双曲柱面；(9)过原点的圆锥面；(10)过原点的椭圆锥面 y2+(1)x+y+z=1,球面；(2)+ (3)y2x2z2=1旋转双叶双曲面；(4)y2z25x旋转抛物面(1)旋转单叶双曲面，它是由双曲线x2y2 z=

或 x=

=1y轴旋转而成旋转抛物面；它由

或 绕z轴旋转而成

z2-

=1z轴旋转而成

或 y= x= 圆锥面，它由相交两直线y=

或x=

z轴旋转而成略

x=23C:y=23sint,t˛[0,2π] z=投影柱面x2y2=12,投影曲线

z=C: 6cost, 6sint,z=2-6cost-6sint,t˛[0,2π]=-2+

=-2+ 投影柱面:xyxy=1投影曲线C:x=cost,y=sint,z=1,t˛[0,2π]

z投影柱面:z=1(-1£y£1),投影曲线:x0,ytz=1,(-1£t£1)C:x=5cost, 5sint, 5sint,t˛[0,2π]=- = xOyzOxyOz上的投影曲线分别为 x cost,y=-

sintz0,t˛[0,2π或

z= x2+y2-3z+1=x cost,y=0,z=

sint,t˛[0,2π或

y=y+z

1+

5-x=0,

sint,t˛[0,2π],(

, £y =-2+

=2

x= 3y2-z2=16,3x2+2z2=16 xOy面上:(x-1)2y2£1.yOz面上:

y2£1.zOx面上:由抛物线z22xzx

C:

C:

2ax-2a(22ax-

y=y+bsinq，(0£q£2π,-¥<t<+¥)0z=

x=y=acoshv，(-¥<u<+¥,-¥<v<+¥z=bsinh

x=asinhucosy=bsinhusinz=–ccoshx=x0+au

y=y0+businq，(0£q£2π,0£u<+¥)z=z+

x=y= z=a2-

x=auy=businq，(0£q£2π,-¥<u