Chapter 15.1, Problem 4ES

Determine whether the statement about the vector field $\text{F(}x,y)$ is true or false. If false. explain why.

$\text{F(}x,y)=\frac{x}{\sqrt{x^2+y^2}}\text{i}-\frac{y}{\sqrt{x^2+y^2}}\text{j}\text{.}$

(a) As $\left(x,y\right)$ moves away from the origin, the lengths of the vectors decrease.

(b) If $\left(x,y\right)$ is a point on the positive $x-\text{axis,}$ then the vector points up.

(c) If $\left(x,y\right)$ is a point on the positive $y-\text{axis},$ the vector points to the right.