Math 208 (Lutz) - Quiz #7, 3/14/14
Name:
Directions: This is a take-home quiz; it is due at the beginning of class on Monday, March 17. You
may consult your class notes and the textbook, and confer with me via e-mail, but you may use no other
resource, electronic or otherwise.
This quiz has 4 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. (4 points) Find parametric equations for the line between the points (1, 2, 5) and (−1, 3, −1).
2. (6 points) The position of a particle is given by the vector !r(t) = "t, t2 , t3 #. Compute the speed of the
particle at time t = −1.
3. (4 points) Sketch the gradient field for the function f (x, y) = −x2 − y 2 .
4. (6 points) Find the flow line of the vector field F! = "2, x# that passes through the point (3, 4) at time
t = 1.