Question

Determine whether the following force field F is conservative: F=xi-yj+zk

Answer 1

Answer:

the curl of F should be zero

Answer 2

Force field is conservative.

Explanation:

Force, F=xi-yj+zk

We need to state weather the force field is conservative or not. For conservative field, its curl is 0. i.e.

$\nabla \times F=0$

$\nabla \times (xi-yj+zk)=0$

$\nabla \times F=\begin{vmatrix}i & j & k\\ \frac{\partial }{\partial x} & \frac{\partial }{\partial y} & \frac{\partial }{\partial z}\\ x &-y & z\end{vmatrix}$

$\nabla\times F=i|\dfrac{\partial z}{\partial y}+\dfrac{\partial y}{\partial z}|-j|\dfrac{\partial z}{\partial x}-\dfrac{\partial x}{\partial z}|+k|\dfrac{\partial (-y)}{\partial x}-\dfrac{\partial x}{\partial y}|$

$\nabla \times F=0$

Hence, force field is conservative.

Learn more,

Curl

https://brainly.in/question/15977216