Do two magnets create magnetic force fields that allow them to interact without touching?

Yeup

Explanation:

if you flip two magnets around so that they're both negative or both positive they have a strong magnetic force that pushes them away from each other without even having to touch

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west