Final answer:
Work in physics is the dot product of force and displacement, resulting in a scalar quantity that represents the work done, this explains why the direction is 'lost' in this operation. The dot product is dependent on the magnitudes and the cosine of the angle between the vectors, with work being positive, negative, or zero depending on the direction of the force relative to displacement.
Step-by-step explanation:
The question involves the concept of work in physics, where work is defined as the dot product of the force vector and the displacement vector. The dot product relates these two vectors to give a scalar quantity which is the work done. Since work is a scalar, it does not have a direction. The result of a dot product depends on both the magnitudes of the vectors and the cosine of the angle between them. If the angle is 0° (force and displacement are in the same direction) or 180° (opposite direction), the work done is maximal (positive or negative, respectively), and if the angle is 90° (force is perpendicular to displacement), the work done is zero.
In the given example, to compute the work done by a force, we need to consider the component of the force in the direction of the displacement. This component is given by the magnitude of the force multiplied by the cosine of the angle between the force and the displacement vectors. The work done by the force over the displacement is then this component times the magnitude of the displacement. The angle determines the sign of the work: if the force is in the direction of the displacement, the work is positive, and if the force is in the opposite direction of the displacement, the work is negative.