Isolate the cable juncture. Express the tensions in terms of unit vectors. Solve the equilibrium equations. The coordinates of points A, B, C, D are:
A(8, 0, 0,) B(0, 3, 8,) C(0, 2,-6), D(0, -4, 0).
The radius vectors for these points are
By definition, the unit vector parallel to the tension in cable AB is
Carrying out the operations for each of the cables, the results are:
The tensions in the cables are expressed in terms of the unit vectors
The external force acting on the juncture is F = 2000i + 0j + 0k. The equilibrium conditions are
Substitute the vectors into the equilibrium conditions:
The commercial program TK Solver Plus was used to solve these equations. The results are
