- #1
Ed Aboud
- 201
- 0
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] ?
Homework Equations
The Attempt at a Solution
I just don't really understand what is being asked here.
Any help would be appreciated.
Thanks.