Chapter 20.1, Problem 25E

A tornado is formed when a tube of air circling a horizontal axis is tilted up vertically by the updraft from a thunderstorm. If t is time, this process can be modeled by the wind velocity field

$\stackrel{\to }{F}(t,x,y,z)=(\cos t\stackrel{\to }{j}+\sin t\stackrel{\to }{k})\times \stackrel{\to }{r}\text{ and }0\le t\le \frac{\pi }{2}.$

Determine the direction of $\text{curl }\stackrel{\to }{F}$

1. (a) $\text{At }t=0$
2. (b) $\text{At }t=\pi /2$
3. (c) $\text{For }0<t<\pi /2$