Test the vector field F to determine if it is conservative.
-F = xyi + yj + zk
A) Not conservative
B) Conservative

Question

Quizplus · Accepted Answer

To test for conservativeness, we need to check if the curl of F is zero. The curl of F is given by:

curl(F) = (dz/dy - dy/dz) i + (dx/dz - dz/dx) j + (dy/dx - dx/dy) k

Substituting the components of F, we get:

curl(F) = 0i + 0j + (1 - 1)k
curl(F) = 0

Since the curl of F is not zero, F is not a conservative vector field. Therefore, the answer is A) Not conservative.

Test the Vector Field F to Determine If It Is