Fundamentals of Physics Extended (10th Edition)

$+z$
We know that $q$ is positive and we want $\vec{v}\times\vec{B}$ to have the same direction as $\vec{F}$ , which is $-\mathrm{y}$. Now, we will use the right hand rule (see fig. 3.19 on p. 53) as follows: Outstretch your right arm and turn your hand so your thumb points down. The fingers are pointing to the right (the fingers represent $\vec{v}$ in the $+x$ direction, and the thumb $\vec{v}\times\vec{B}$ in the $-y$ direction). Swipe your fingers roughly for a right angle. The fingers now point behind you; This is the +z direction, when compared to the diagram. This is where $\vec{B}$ points.