6.
x2/16+y2/4=1, ellipse
36.
x=aΘ-bsin(Θ), y=a-bcos(Θ)
Section
9.5
2.
–8
18.
7
24.
28π/9
Section
9.6
6.
a) (1,1) b) (1,0) c) (0,0) d) (-1,1) e) (3sqrt(3)/2, -3/2) f) (3,4) g) (1,0)
h)
(-sqrt(3),3)
60.
r=10cos(Θ)
Section
9.9
30.
πsqrt(5)(eπ/2+1)
Section
10.1
20.
u=-1/sqrt(2)i-1/sqrt(2)j
30.
tangent vector 1/sqrt(34)(5i+3j), normal vector 1/sqrt(34)(-3i+5j)
Section
10.3
8.
AB=2, |A|=sqrt(2), |B|=sqrt(3), cos(Θ)=sqrt(2/3), |B|cos(Θ)=sqrt(2),
projAB=i+k
Section
10.4
6.
AxB=j, BxA=-j
Section
10.5
6.
x=3+2t, y=-2-t, z=1+3t
Section
10.7
Rectangular Cylindrical Spherical
2. (1,0,0) (1,0,0)
(1,π/2,0)
4. (0,0,1) (0,0,1)
(1,0,0)
6. (sqrt(2),0,1) (sqrt(2),0,1) (sqrt(3),cos(1/sqrt(3)),0)
8. (0,-3/2,sqrt(3)/2)
(3/2,3π/2,sqrt(3)/2) (sqrt(3),π/3,-π/2)
10. (0,0,-sqrt(2)) (0,0,-sqrt(2)) (sqrt(2),π,3π/2)
32.
A cone with vertex (0,0,4) (rectangular) and base the circle x2+y2=16
in the xy-plane
40.
Right circular cylinder parallel to the z-axis generated by the circle
r=2cos(Θ) in the rΘ-plane