Vector Calculus: Gradient, Divergence, and Curl — Engineering Board Exam Practice Questions

6 free engineering board exam reviewer questions on Vector Calculus: Gradient, Divergence, and Curl (Advanced Engineering Mathematics), each with the correct answer and a worked solution.

1. Evaluate C(x,dy-y,dx) counterclockwise around the circle x2+y2=4.
2. The field F=(2xy+z3), i+x2, j+3xz2, k is conservative. Find a scalar potential with F= .
3. Find the directional derivative of =x2+yz at (1,2,1) in the direction of i+2 j+2 k.
4. Find × F if F=y2z, i+xz2, j+x2y, k.
5. Find · F if F=x2y, i+yz2, j+xz, k.
6. Find if =x2y+z.