Final answer:
A tension cable must be used when pulleys are used to change the direction of cable travel. Tension is the force transmitted through the cable, and it is always in the direction parallel to the cable.
Step-by-step explanation:
The type of control cable that must be used when pulleys are used to change the direction of cable travel is a tension cable. Tension is the force transmitted through the cable, and it is always in the direction parallel to the cable.
When tension is applied, it pulls outward along the two ends of the cable, allowing the pulleys to change the direction of the force without changing its magnitude.