A particle is moving on frictionless XY-plane. It is acted on by a conservative force described by the potential-energy function.
`U(x,y,z)=(1)/(2)k(x^(2)+y^(2)+z^(2))`
where , k=constant
Derive an expression for the force an the particle.

Explanation

To derive the expression for the force acting on the particle from the given potential energy function, we can follow these steps:

### Step 1: Understand the relationship between force and potential energy
The force acting on a particle in a conservative field can be derived from the potential energy function \( U(x, y, z) \) using the formula:
\[ \vec{F} = -\nabla U \]
where \( \nabla U \) is the gradient of the potential energy function.
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