Question

Given F1=2xi-2yzj-y^2k and F2=yi-xj,
Are these forces conservative?

Answer 1

I want to use the method of curl F, where the operator multiplied by F would tell me if it is conservative IF it equals 0

Answer 2

$$
if~ g(x,y,z)=x^2-y^2z-y^3/3\\
then ~\nabla g=F_1
$$
So F1 is conservative.
For F2:
$$
\partial M/\partial y=1\\
\partial N/\partial x=-1
$$
Since these are not equal, F2 is not conserviative.

Answer 3

I need those steps broken down alittle more please if you can

Answer 4

you should take curl of those force
f1 is concerviative because:
((d/dy)(-y^2)-(d/dz)(-2yz))i+((d/dz)(-2x)-(d/dx)(-y^2))j+((d/dx)(-2yz)-(d/dy)(-2x))k
-2y+2y+0+0=0
so f1 is concervative

Answer 5

but f2 is not concervative because curl f2=-2