Please solve using forces and equilibrium to the case of thr

Please solve using forces and equilibrium to the case of three dimensional problems. I will for sure rate. Thanks.

2. The package is being pulled at point A by cable AB. For what tensile force in the cable will the x-component of the force exerted by the cable on the package be 200 N?

Solution

Coordinate of A=(0,0.2,0.6)

Coordinate of B=(0.9,0,0)

vector AB = 0.9i-0.2j-0.6k

unit vector along AB = (0.9i-0.2j-0.6k)/sqrt(0.9²+0.2²+0.6²)=(0.9i-0.2j-0.6k)/1.1

Let magnitude of force in cable be F

In vector notation,F=F*(0.9i-0.2j-0.6k)/1.1

x component of force = F*(0.9/1.1)=200

F=200*1.1/0.9=244.44 N

Therefore,force in cable shoulb be equal to 244.44 N