A tornado is formed when a tube of air circulating a horizontal axis is tilted up vertical by the updraft from a thunderstorm. If $t$ is time, this process can be modeled by the wind velocity field $$\vec{F}(t,x,y,z) = (\cos(t)\vec{j} + \sin(t)\vec{k}) \times \vec{r} \quad \mbox{ and } \quad 0 \leq t \leq \pi/2.$$
(a) $\mathrm{curl}(\vec{F}(t,x,y,z))$ =

(b) Find $\mathrm{curl}(\vec{F}(0,x,y,z))$ =
In which direction does this vector point (horizontal, vertical, or in betweeen)? Choose horizontal vertical in between

(c) Find $\mathrm{curl}(\vec{F}(\pi/6,x,y,z))$ =
In which direction does this vector point (horizontal, vertical, or in betweeen)? Choose horizontal vertical in between

(d) Find $\mathrm{curl}(\vec{F}(\pi/2,x,y,z))$ =
In which direction does this vector point (horizontal, vertical, or in betweeen)? Choose horizontal vertical in between