electron in magnetic and electric field

I have this problem where i should find the direction and magnitude of the electric and the magnetic force on the electron. And then I'm supposed to find the direction and magnitude of the acceleration.
E = 1000 N/m B = 2,5 T v = 500 m/s

X |X X| X
 ¤->
X |X X| X
X |X X| X
  V   V

I've found the electric force by Fe = E*q. With direction out of the screen by the right hand rule. Magnetic force = qvb in the y direction (meaning up) by the right hand rule. Now Im supposed to find the acceleration but I'm a bit stuck here. What i'm struggling with is to combine the two forces on the electron. Can someone get me in the right direction?

Answer

You just use vector addition and Newton's Second Law. For example, if you have

$$\overrightarrow{F}_E=qE\hat{x},\space\space\space\overrightarrow{F}_B=qvB\hat{y}$$ then your total force $F_{tot}=F_E+F_B$ is just $$\overrightarrow{F}_{tot}=qE\hat{x}+qvB\hat{y}$$ Since $\hat{x}$ and $\hat{y}$ are totally linearly independent, these terms cannot be combined. Then using $F=ma$ you can deduce that $$\overrightarrow{a}=\frac{q}{m}(E\hat{x}+vB\hat{y})$$ but if you wanted the magnitude of the acceleration, you just take $$a=\sqrt{\overrightarrow{a}\cdot\overrightarrow{a}}=\frac{q}{m}\sqrt{E^2+v^2B^2}$$