Vector Fields

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Objectives:

1.: Know what a vector field is and how to visualize one.

Recap Video

The following video recaps the ideas of the section.

Problems

Given a function $f(x,y)$ whose partials are continuous everywhere, which of the following represents a vector field. Select all that apply.

The function $f(x,y)$ The gradient $\nabla f(x,y)$ The partial derivative $f_x(x,y)$ The function $\textbf {F}(x,y) = \left \langle f_y(x,y),1 \right \rangle$

Which of the following represents the full domain of the vector field $\textbf {F}(x,y) = \left \langle \frac {1}{x},y \right \rangle$ ?

All points $(x,y)$ . All points $(x,y)$ except the origin. All points $(x,y)$ except the line $x=0$ .

The vector field $\textbf {F} = \left \langle x-y,1 \right \rangle$ corresponds to which of the following figures?
The vector field $\textbf {F} = \left \langle x+y,1 \right \rangle$ corresponds to Figure:
The vector field $\textbf {F} = \left \langle x,-y \right \rangle$ corresponds to Figure: