Solutions to Quiz 5 Sample B - Loyola University Chicago
Loyola University Chicago Math 263, Fall 2011 Name (print): Quiz 5 Sample B Solutions Signature: You have 30 minutes. Show your work. Notes not allowed! Problems are on both sides of this sheet. Problem 1. (5 pts) Find the work done by the force F = 2yi + 3xj + (x + y)k over the helix r(t) = 〈cost, sint, t/6〉, 0 ≤ t ≤ 2π. Hint: see Example 6, section 16.2 of the textbook, page 915. That example is very similar. ∮ Problem 2. (5 pts) Find 0 ≤ t ≤ 2π C F · dr where F = 〈2x, 3y, 4z〉and C is the circle r(t) = 〈14 cost, 14 sint, 0〉, Solution: the vector field F is conservative. Indeed, F = ∇f for f(x, y, z) = x 2 + 3 2 y2 + 2z 2 . The curve C is closed, hence the integral is 0.