Chapter 9.FOM, Problem 1P

To determine

To sketch:

The vector field $F$.

Answer to Problem 1P

Solution:

The diagram for the vector field $F$ is shown in figure $\left(1\right)$.

Explanation of Solution

Given:

The vector field is $F\left(x,y\right)=\frac{1}{2}i+\frac{1}{2}j$.

Approach:

The vector field in the coordinate plane is a function that assigns a vector to each point in the plane. Such as,

$F\left(x,y\right)=xi+yj$ ……$\left(1\right)$

Calculation:

Compare the force vector with equation $\left(1\right)$. This gives,

$x=\frac{1}{2},y=\frac{1}{2}$

The diagram for the vector field $F$ is shown below,

Figure $\left(1\right)$

Therefore, the diagram for the vector field $F$ is shown in figure $\left(1\right)$.

Conclusion:

Hence, the diagram for the vector field $F$ is shown in figure $\left(1\right)$.