Math 208 (Lutz) - Quiz #3, 1/31/14
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. (5 points) Consider the following contour diagram for the function z = f (x, y). Is fy (−2, 1) positive,
negative, or zero? Briefly justify your answer.
2. (7 points) For the vectors !a = !i − !j + 2!k and !b = 3!i + !j + !k, calculate the cross-product !a × !b.
3. (8 points) Write !v = !1, −1, 3# as the sum of two vectors, one parallel, and one perpendicular to,
w
! = !4, −2, 4#. Hint: ||w||
! = 6.