1. Find the center of mass of the masses located as follows: 3 kg at (-2,3), 2 kg at (2,-3), 4 kg at (1,0).
2. Find the center of mass of the region bounded by y = sin x, y =, and between x=0 and x=¹.
3. Find the center of mass of the volume obtained by rotating the region bounded by y = ln x, y = 0, between x = 1 and x = e about the y axis.
4.a) Change the point (-3,-5) to polar form.
b) Change the point (-2,240) to rectangular form.
5.a) Change the equation x2 - y2 =2 to polar form.
b)Change the equation r = 3cos u to rectangular form.
6. Sketch the graph of r = 1+ cos 2u:
a) first on r vs q graph
b) then polar graph on xy plane.
7. Find the points of intersection of r1 = cos u and r2 = 1 - cos u.
Given A = (3,-2,4) and B = (5,4,-1), find:
8. The vector AB
9. The point P on the line AB such that AP/AB = 3.
Considering the vector A = <1,0,2> and B = <3,-4,2>, find:
10. The unit vector in the direction of A.
11. The projection of A onto B.
12. A.B=
13. The angle between A and B.
14. Find a so that U = ai- j and V = 3i + aj are parallel.
10 Points Bonus !!
Change the equation r = sin 2u to rectangular form.