Math 208 (Lutz) - Quiz #9, 11/01/13
Name:
Directions: This quiz has 3 questions, for a total of 20 points. Solve each problem carefully. You must
show ALL of your work in order to earn full credit.
1. (3 points) Give an example of a vector field F! (x, y) with the property that all vectors are parallel to
the line y = 2x.
2. (6 points) Consider motion given by the vector equation
!r(t) = 2!i + 6!j + (t3 + t)(4!i + 3!j + !k).
Compute the acceleration vector !a(t).
3. (7 points) Two particles travel through space. Their positions at time t are given by (1+t, 2−t, 3+2t),
and (5 − t, 2 − 3t, 3 + 6t), respectively. Do the paths of the particles cross? If so, where do the paths
cross?
4. (6 points) The velocity of a flow at the point (x, y) is F! (x, y) = x!j. Find the path of motion of an
object in the flow that is at the point (2, 3) at time t = 1.