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
  r_A = 175i + 0j + 0k m
  r_B = 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.