- #1
slonopotam
- 6
- 0
[tex]\vec{F}=(\frac{x}{\sqrt{x^2+y^2+z^2}},\frac{y}{\sqrt{x^2+y^2+z^2}},\frac{z}{\sqrt{x^2+y^2+z^2}})[/tex]
[tex]
\vec{r}=(x,y,z)
[/tex]
[tex]
|r|=\sqrt{x^2+y^2+z^2}[/tex]
[tex]\vec{F}=(\frac{x}{|r|},\frac{y}{|r|},\frac{z}{|r|})[/tex]
so its [tex]F=\frac{r}{|r|}[/tex]
i need to prove that F is a conservative field
where (x,y,z) differs (0,0,0)
so i need to show that rot f is 0
but for rottor i need a determinant
is there a way to do a rot on simpler way?
[tex]
\vec{r}=(x,y,z)
[/tex]
[tex]
|r|=\sqrt{x^2+y^2+z^2}[/tex]
[tex]\vec{F}=(\frac{x}{|r|},\frac{y}{|r|},\frac{z}{|r|})[/tex]
so its [tex]F=\frac{r}{|r|}[/tex]
i need to prove that F is a conservative field
where (x,y,z) differs (0,0,0)
so i need to show that rot f is 0
but for rottor i need a determinant
is there a way to do a rot on simpler way?