Answer
Consider, $f,g,h$ be defined on a region $D$ of $R^{3}$.\\
A vector field in $R^{3}$ is s function $F$ that assigns to each point in $D$ vectors
\begin{align*}
\langle f(x,y,z),g(x,y,z), h(x,y,z)\rangle.
\end{align*}
The vector field is written as follows:
\begin{align*}
F(x,y,z)&=f(x,y,z)i+g(x,y,z)j+h(x,y,z)k.
\end{align*}
The vector field $F=\langle f,g,h\rangle$ evaluated at $(x,y,z)$ is the velocity vector of an air particle at $(x,y,z)$ a fixed point in time.
Work Step by Step
Consider, $f,g,h$ be defined on a region $D$ of $R^{3}$.\\
A vector field in $R^{3}$ is s function $F$ that assigns to each point in $D$ vectors
\begin{align*}
\langle f(x,y,z),g(x,y,z), h(x,y,z)\rangle.
\end{align*}
The vector field is written as follows:
\begin{align*}
F(x,y,z)&=f(x,y,z)i+g(x,y,z)j+h(x,y,z)k.
\end{align*}
The vector field $F=\langle f,g,h\rangle$ evaluated at $(x,y,z)$ is the velocity vector of an air particle at $(x,y,z)$ a fixed point in time.
