Set the coordinate origin at A with axes as shown. The upward force, T, at point A will be equal to the weight, W, since the cable at A supports the entire wall. The upward force at A is T = W k. From the figure, the coordinates of the points in metre are
A(4,6,10) B(0,0,0) C(12,0,0) and D(4,14,0).
The three unit vectors are of the form
where I takes on the values B, C, and D. The denominators of the unit vectors are the distances AB, AC, and AD, respectively. Substitution of the coordinates of the points yields the following unit vectors:
The equilibrium equation for the knot at point A is
T + TAB + TAC + TAD = 0.
From the vector equilibrium equation, write the scalar equilibrium equations in the x, y, and z directions. We get three linear equations in three unknowns. Solving these equations simultaneously, we get
TAB = 9393 N, TAC = 5387 N, and TAD = 10,977 N.