(1 point) A tornado is formed when a tube of air circulating a horizontal axis is tilted up vertical by the updraft from a thunderstorm. If tt is time, this process can be modeled by the wind velocity field
F⃗ (t,x,y,z)=(cos(t)j⃗ +sin(t)k⃗ )\times r⃗ and 0<=t<=(\pi )/(2.)F->(t,x,y,z)=(cos(t)j->+sin(t)k->)\times r-> and 0<=t<=(\pi )/(2.)
(a)curl(F⃗ (t,x,y,z))curl(F->(t,x,y,z))=0i+0j+0k
(b) Findcurl(F⃗ (0,x,y,z))curl(F->(0,x,y,z))=0i+0j+0k
In which direction does this vector point (horizontal, vertical, or in betweeen)? Choose horizontal vertical in between
(c) Findcurl(F⃗ ((\pi )/(4),x,y,z))curl(F->((\pi )/(4),x,y,z))=0i+0j+0k
In which direction does this vector point (horizontal, vertical, or in betweeen)? Choose horizontal vertical in between
(d) Findcurl(F⃗ ((\pi )/(2),x,y,z))curl(F->((\pi )/(2),x,y,z))=0i+0j+0k
In which direction does this vector point (horizontal, vertical, or in betweeen)? Choose horizontal vertical in between
Note: r⃗ r-> is the position vector (x,y,z)(x,y,z).
