Option 1: Perpendicular to each other - When the applied force and displacement are perpendicular to each other, the work done would be zero. This is because there is no component of the force that is acting in the direction of the displacement.

Option 2: Parallel to each other - When the applied force and displacement are parallel to each other, the work done would be positive. This is because the force is acting in the same direction as the displacement, resulting in a positive work done.

Option 3: Anti-parallel to each other - This is the correct answer. When the applied force and displacement are anti-parallel to each other, the work done would be negative. This means that the force is acting in the opposite direction of the displacement, resulting in a negative work done.

Option 4: Equal in magnitude - The magnitude of the force and displacement being equal does not determine if the work done is positive or negative. The direction of the force with respect to the displacement is what determines the sign of the work done.

In summary, a negative work is done when the applied force and displacement are anti-parallel to each other, meaning the force acts in the opposite direction of the displacement.