A mobility vector is calculated as the resultant vector derived from three given vectors, v1, v2, and v3, in Cartesian format. To find the resultant vector, one must use the components method, breaking each vector into horizontal (x) and vertical (y) components. By summing all x components and all y components separately, a new vector representing the mobility vector can be obtained. Basic trigonometry is necessary for this calculation, and reference to a physics textbook may provide additional clarity. Understanding the mobility vector involves recognizing it as a single unit representing the combined effect of the three vectors.