Work done ($W$) is given by the formula $W = F \cdot d \cdot \cos(\theta)$, where $F$ is the magnitude of the force, $d$ is the magnitude of the displacement, and $\theta$ is the angle between the force and displacement vectors. When the force and displacement are perpendicular, $\theta = 90^\circ$, and $\cos(90^\circ) = 0$, so the work done is zero.