Final answer:
To project force F onto cable AC, calculate the unit vector in the direction of AC and multiply it by the magnitude of F. Without specific direction details of AC, the exact numerical value of the projection cannot be provided.
Step-by-step explanation:
To determine the projected component of the force F = 12 lb acting in the direction of cable AC, we need to find the unit vector in the direction of AC and multiply it by the magnitude of F. Since the unit vector r has a magnitude of 1 and points in the specific direction of interest, we can calculate the projection of F onto r using the dot product if both vectors are in Cartesian form, or simply multiply the magnitude of F by the unit vector if only the direction is specified. Without the coordinates or direction angles for AC, we cannot provide a numerical answer but can offer the formula for the projection of F onto the cable AC, denoted as FAC, which is FAC = F · unit_vector_AC.