1. Problem 3.149 y C 10 ft The 15-ft boom AB has a fixed 6 ftz
15 ft
6 ft
10 ft
The 15-ft boom AB has a fixed
end A. A steel cable is stretched
from the free end B of the boom
to a point C located on the
vertical wall. If the tension in the
cable is 570 lb, determine the
moment about A of the force
exerted by the cable at B.

2. F d y C Solving Problems on Your Own 10 ft 6 ftA x y z
15 ft
6 ft
10 ft
Solving Problems on Your Own
The 15-ft boom AB has a fixed
end A. A steel cable is stretched
from the free end B of the boom
to a point C located on the
vertical wall. If the tension in the
cable is 570 lb, determine the
moment about A of the force
exerted by the cable at B.
Problem
1. Determine the rectangular components of a force defined by
its magnitude and direction. If the direction of the force is
defined by two points located on its line of action, the force can
be expressed by:
F = Fl = (dx i + dy j + dz k) F d

3. Solving Problems on Your OwnC B A x y z
15 ft
6 ft
10 ft
Solving Problems on Your Own
The 15-ft boom AB has a fixed
end A. A steel cable is stretched
from the free end B of the boom
to a point C located on the
vertical wall. If the tension in the
cable is 570 lb, determine the
moment about A of the force
exerted by the cable at B.
Problem
2. Compute the moment of a force in three dimensions. If r is a
position vector and F is the force the moment M is given by:
M = r x F

4. TBC = (_15 i + 6 j _ 10 k) = _ (450 lb) i + (180 lb) j _ (300 lb)k
570 N C B A x y z
15 ft
6 ft
10 ft
Problem Solution
Determine the rectangular
components of a force defined
by its magnitude and direction.
First note:
dBC = (_15)2 + (6) 2 + (_10) 2
dBC = 19 ft
Then:
TBC = (_15 i + 6 j _ 10 k) = _ (450 lb) i + (180 lb) j _ (300 lb)k
570 lb 19

5. MA = rB/A x TBC MA = 15 i x (_ 450 i + 180 j _ 300 k)
570 N C B A x y z
15 ft
6 ft
10 ft
Problem Solution
Compute the moment of a
force in three dimensions.
Have:
MA = rB/A x TBC
Where: rB/A = (15 ft) i
Then:
MA = 15 i x (_ 450 i j _ 300 k)
MA = (4500 lb.ft) j + (2700 lb.ft) k