Posted: July 17th, 2021

To find a force’s directional components that act along a cable and to find the coordinates of a point on a cable that has a force vector applied to it.

Three-dimensional Cartesian force vectors are used throughout engineering mechanics. The generic force vector is represented as follows:

F=Fxi+Fyj+Fzk

where F is the force vector and Fx, Fy, and Fz are the vector’s i, j, and k components, respectively. The force vector has a magnitude F=F2x+F2y+F2z−−−−−−−−−−−−√. The vector’s direction is described by a unit vector u, where u=F/F.

As shown, a force vector F with a magnitude of c = 33.0 lb is applied at point *A* and is directed toward point *C*. (Figure 1) The distance a is 2.00 ft and the distance b is 5.50 ft . What are the i, j, and k components of F?

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