Construction Trolley System
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Displacement Vectors


Some workers are refurbishing the Eiffel Tower. The construction crew utilizes a trolley system to transport equipment from point A on the ground to point B on the platform they are working on. The trolley is pulled by two cables at the base of the tower.

What is known:

  • With an axis system oriented as shown, the position vectors of points A and B are
    rA = 175i + 0j + 0k m
    rB = 39i + 70j + 29k m

  • When the trolley is halfway between points A and B, the forces exerted on the trolley by the cables are
    F1 = -943.7i - 221.7j + 245.4k m
    F2 = -919.4i - 216.0j - 328.6k m


What is the component of the force exerted on the trolley that is parallel to the line AB?


  • Find the unit vector in the direction of the line AB.
  • Find the total force exerted on the trolley by the two cables.
  • Solve for the component of the total force that is parallel to the unit vector for line AB.