F(x, y, z) = xyz i + (y - 5) j + (z + 5) k. Find curlF.
A) xz i
B) xz i - z j
C) xy j - xz k
D) xy j + xz k
E) xz i + z j

Question

Quizplus · Accepted Answer

The curl of F is defined as:

curlF = (dFz/dy - dFy/dz) i + (dFx/dz - dFz/dx) j + (dFy/dx - dFx/dy) k

Taking partial derivatives of F, we get:

dFx/dy = xz
dFx/dz = xy
dFy/dx = 0
dFy/dz = 1
dFz/dx = 0
dFz/dy = 0

Substituting these values into the formula for curlF, we get:

curlF = (0 - 0) i + (xy - 0) j + (0 - xz) k
      = xy j - xz k

Thus, the best choice is C.

F(x, Y, Z) = Xyz I + (Y - 5)