Chapter 15.1, Problem 3ES

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

$\begin{array}{l}\text{F}\left(x,y\right)=x^2\text{i}-y\text{j}\\ \left(\text{a}\right)‖\text{F}\left(x,y\right)‖\to 0\text{as}(x,y)\to (0,0).\end{array}$

(b) $\text{If}(x,y)$ is on the positive y-axis, then the vector points in the negative y-direction.

(c) $\text{If}(x,y)$ is in the first quadrant, then the vector points down and to the right.