Question

Short answer

Step-by-Step Solution

Step-by-step solution

Concept

To sketch a vector field, draw the arrow representing the vector\({\rm{F}}\left( {{\rm{x,y}}} \right){\rm{ = 0}}{\rm{.3i - 0}}{\rm{.4j}}\)starting at point\(\left( {{\rm{x, y}}} \right)\).

It is impossible to do this for all points\(\left( {{\rm{x, y}}} \right)\)but we can gain a reasonable impression of\({\rm{F}}\)by doing it for a few representative points in the domain.

Given Information.

The given vector field is \(F\left( {x,y} \right) = 0.3i - 0.4j\).

Calculation.

We will first calculate several representative values of \(F\left( {x,y} \right)\) in the table form, and then, by using the concept, draw the corresponding vectors to represent the vector field.

Several representative values of \(F\left( {x,y} \right)\) are:

\(\left( {x,y} \right)\)	\(F\left( {x,y} \right)\)
\((1,0)\)	\((0.3, - 0.4)\)
\((1,1)\)	\((0.3, - 0.4)\)
\((0,1)\)	\((0.3, - 0.4)\)
\(( - 1,1)\)	\((0.3, - 0.4)\)
\(( - 1,0)\)	\((0.3, - 0.4)\)
\(( - 1, - 1)\)	\((0.3, - 0.4)\)
\((0, - 1)\)	\((0.3, - 0.4)\)
\((1, - 1)\)	\((0.3, - 0.4)\)

Sketch the vector field.

The sketch of the vector will be:

The sketch of the vector field will be: