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**1. Homework Statement**

Let [tex] r = \sqrt{x^2 +y^2 +z^2} = \lVert x \rVert _\mathbb{R} _^3 [/tex]

be the Euclidean distance of the point [tex] x = (x,y,z) \in \mathbb{R} ^3 [/tex] from the origin.

And [tex] e_r := \nabla r[/tex]

Let

**F**be a

*central force*, i.e.,

[tex] \underline{F} = - \nabla U(r) [/tex]

for some function [itex] U : \mathbb{R} \rightarrow \mathbb{R} [/itex]

Show that

[tex]\underline{F} = \pm \lVert \underline{F} \rVert e_r [/tex]

What is [tex]\lVert F \rVert [/tex] ?

**2. Homework Equations**

**3. The Attempt at a Solution**

I just don't really understand what is being asked here.

Any help would be appreciated.

Thanks.