Bloons Monkey City – Castle City Walls Hack MOD Free Download

 

 

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“Direction” of a vector field $\mathbf{F}$ (lacks uniqueness)

I have a question about vector fields:
Lets say that $U$ is an open subset of $\mathbb{R}^3$, $\mathbf{F}:U\to\mathbb{R}^3$ is a vector field and $\sigma:U\to\mathbb{R}$ is a scalar-field. Does there exist another (possibly other than $\mathbf{F}$) vector field $\mathbf{G}:U\to\mathbb{R}^3$ satisfying the following conditions:

$\mathbf{G}(U)\subset U$
$\mathbf{G}$ is differentiable
$\mathbf{G}(x)\cdot\mathbf{F}(x)\ge\sigma(x)$ for all $x\in U$.

As an example, $\mathbf{F}$ could be defined by $\mathbf{F}(x)=\begin{pmatrix}x\\0\\0\end{pmatrix}$ for all $x\in U$ and $\sigma(x)=x$ for all $x\in U$.
I’m wondering whether this is possible or not, but cannot find a counterexample.
Thanks for your time!

A:

Consider the vector field $$\mathbf{G}(x) = \begin{cases} \mathbf{F}(x) & \text{if } x \in U \\

 

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    Basic Information

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    Bloons Monkey City – Castle City Walls Crack + With License Key Free

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