Step 1: Recall the magnetic force.
A charge $q$ moving with velocity $v$ in a magnetic field $B$ feels a force \[ F = qvB\sin\theta \] where $\theta$ is the angle between the velocity and the field.
Step 2: Find what controls the size.
Here $q$, $v$, and $B$ are fixed for the problem. So the force only changes with the $\sin\theta$ part.
Step 3: Maximize the sine.
The sine function is largest when it equals one. This happens at \[ \theta = 90^\circ \]
Step 4: Write the maximum force.
At ninety degrees, \[ F_{max} = qvB \] because $\sin 90^\circ = 1$.
Step 5: Check the small angles.
At zero or one hundred eighty degrees the sine is zero, so the force is zero. So those give the weakest, not the strongest, force.
Step 6: State the answer.
The force is largest when the velocity is at right angles to the field. \[ \boxed{\theta = 90^\circ} \]