Answer
$v = 4.22\times 10^6~m/s$
Work Step by Step
If the net force is zero, the magnitude of the force from the magnetic field must be equal in magnitude to the force from the electric field.
We can find the speed of the electron:
$q~v~B = E~q$
$v = \frac{E}{B}$
$v = \frac{2.68\times 10^6~V/m}{0.635~T}$
$v = 4.22\times 10^6~m/s$
