Math 210 Practice Problems
Exam 1 Material
Note: This is not an exhaustive list of problems, nor is it in the format of the
exam. It is just some practice problems to act as a study aid.
For the problems 1-6 use ~v = (1,6,2) and ~w = (3,0,−1)
1. Draw ~v, ~w, ~v +~w, and ~v −~w.
2. Find the equation(s) for the line in the direction of ~v +~w and through the point
(3,4,5).
3. Find the angle between ~v +~w and ~v −~w.
4. Find a unit vector perpendicular to both ~v and ~w.
5. Find the equation for the plane which contains the endpoints of ~v and ~w (in-
cluding the origin).
6. Find the projection of ~v onto ~w. How is this different from the component of ~v
in the direction of ~w.
7. If ||~u|| = 3,||~q|| = 2,and θ=π/6 where θis the angle between ~u and ~q compute
||~u ·~q||
||~u ×~q|| =
8. Find the equation(s) for the surface z2=x2+y2in both cylindrical coordinates
and spherical coordinates.
9. Parameterize the curve formed by the intersection of the cylinder x2+y2= 4
and the sphere (x−2)2+y2+z2= 1.
1
