Three cables support a hanging point O, from which a massive sphere M of weight W=100N, hangs as in the figure. The cables connect point O with points A and B in the ceiling and point C on the right wall. The points have the following coordinates in meters:

O: (1.50,1.50,0.80)

A: (0.50,1.00,3.00)

B: (2.50,2.80,3.00)

C: (3.00,0.50,2.50)

 

T is the tension per length in cable, (T-force/length). Equilibrium at point O means that the net force of the three cables exactly compensate the weight of M: eq1: F-A(+FB+FC+F-GrM=0- It is easy to realize that: F-A=TA(A-O) 1. Show that (eq1) is equivalent to a linear system of 3 equations with the unknowns: TA, TB and TC. Call the coefficient matrix C and the augmented matrix G. 2. Calculate the determinant of the coefficient matrix C