Greg Esres wrote:

Tower guys don't give headings, they give vectors

Nonsense. Vectors require radar contact, and lots of towers aren't
associated at all with any radar facility.

Vectors do not require radar contact when issued with your takeoff
clearance. There are rules as to how soon after you takeoff that you
must be seen on the radar, otherwise the controller cannot vector you.
The tower itself does not have to have radar to give you a vector. If
the approach control can see aircraft within a half a mile after takeoff
they may have the tower give you a vector.