142
2–121.
Determine the angle between the two cables attached to
the pipe.
u
SOLUTION
60
z
60
F
2
25 lb
u
Unit Vectors:
The Angles Between Two Vectors :
u
Ans:
143
2–122.
Determine the angle
u
between the cables AB and AC.
SOLUTION
Unit Vectors. Here, the coordinates of points A, B and C are
A(6, 0, 0) m
,
B(0, –1, 2) m
and
C(0, 1, 3)
respectively. Thus, the unit vectors along
AB and AC are
The Angle
u
Between AB and AC.
z
A
B
C
D
y
x
3 m
6 m
1 m
2 m
1 m
Fu
144
Ans:
2–123.
Determine the magnitude of the projected component of the
force F = {400i – 200j + 500k} N acting along the cable BA.
SOLUTION
Unit Vector. Here, the coordinates of points A and B are
A(6, 0, 0) m
and
z
A
B
C
D
y
x
3 m
6 m
1 m
2 m
1 m
Fu
Ans:
*2–124.
Determine the magnitude of the projected component of the
force F = {400i – 200j + 500k} N acting along the cable CA.
SOLUTION
Unit Vector. Here, the coordinates of points A and C are
A(6, 0, 0) m
and
C(0, 1, 3) m
respectively. Thus, the unit vector along CA is
z
A
B
C
D
y
x
3 m
6 m
1 m
2 m
1 m
Fu
146
2–125.
Determine the magnitude of the projection of force
along the axis.uF =600 N
SOLUTION
Unit Vectors: The unit vectors and must be determined first.From Fig. a,
uu
uOA
2 m
4 m
4 m
F 600 N
z
O
y
A
Ans:
147
2–126.
Determine the magnitude of the projected component of
the 100-lb force acting along the axis BC of the pipe.
Ans:
z
y
D
3 ft
6 ft
4 ft
8 ft
F 100 lb
A
B
2 ft
u
x
SOLUTION
148
2–127.
Determine the angle
u
between pipe segments BA and BC.
Ans:
z
y
D
3 ft
6 ft
4 ft
8 ft
A
B
u
x
149
*2–128.
Determine the angle
u
between BA and BC.
SOLUTION
Unit Vectors. Here, the coordinates of points A, B and C are
A(0, –2, 0) m,
B(0, 0, 0) m
and
C(3, 4, –1) m
respectively. Thus, the unit vectors along
BAandBC are
y
C
B
A
D
z
3 m
2 m
1 m
4 m
5 m
xF 3 kN
u
150
Ans:
2–129.
Determine the magnitude of the projected component of the
3kN force acting along the axis BC of the pipe.
SOLUTION
Unit Vectors. Here, the coordinates of points B, C and D are B (0, 0, 0) m,
C(3, 4, –1) m
and
D(8, 0, 0).
Thus the unit vectors along BC and CD are
Projected Component of F. Along BC, it is
y
C
B
A
D
z
3 m
2 m
1 m
4 m
5 m
xF 3 kN
u
151
2–130.
Determine the angles and made between the axes OA
of the flag pole and AB and AC, respectively, of each cable.
fu
SOLUTION
4m
C
B
z
F
C
40 N
2m
1.5 m
152
2–131.
Determine the magnitudes of the components of acting
along and perpendicular to segment BC of the pipe
assembly.
F
SOLUTION
Unit Vector: The unit vector must be determined first.From Fig. a
Ve ctor Dot Product: The magnitude of the projected component of parallel to
segment BC of the pipe assembly is
F
uCB
y
x
z
A
B
4 ft
2 ft
4 ft
3 ft
F {30i 45j 50k} lb
Ans:
153
*2–132.
Determine the magnitude of the projected component of
along AC.Express this component as a Cartesian vector.
F
SOLUTION
Unit Vector: The unit vector must be determined first.From Fig. a
uAC
y
x
z
A
B
4 ft
2 ft
4 ft
3 ft
F {30i 45j 50k} lb
Ans:
154
2–133.
Determine the angle between the pipe segments BA and BC.
u
SOLUTION
Position Vectors: The position vectors and must be determined first.From
Fig. a,
Vector Dot Product:
rBC
rBA
y
x
z
A
B
4 ft
2 ft
4 ft
4 ft
3 ft
F {30i 45j 50k} lb
155
SOLUTION
Use the x, y, z axes.
2–134.
If the force F = 100 N lies in the plane DBEC, which is
parallel to the x–z plane, and makes an angle of 10
°
with the
extended line DB as shown, determine the angle that
F makes with the diagonal AB of the crate.
Ans:
30
F
2
6 kN
0.5 m
F
B
C
A
x
y
E
0.2 m
15
z
z¿
15
10u
0.2 m
D
2–135.
Determine the magnitudes of the components of force
acting parallel and perpendicular to diagonal AB
of the crate.
F=90 lb
SOLUTION
Force and Unit Vector: The force vector and unit vector must be determined
first.From Fig. a
Ve ctor Dot Product: The magnitude of the projected component of parallel to the
diagonal AB is
F
uAB
F
1 ft
60
45
F 90 lb
A
C
B
x
z
y
1.5 ft
3 ft
157
*2–136.
SOLUTION
Force Vector: The force vector Fmust be determined first. From Fig. a,
Determine the magnitudes of the projected components of
the force acting along the xand yaxes.F=300 N
z
A
O
300 mm
300 mm
F300 N
30
30
Ans:
158
2–137.
z
A
O
xy
300 mm
300 mm
300 mm
F300 N
30
30
Determine the magnitude of the projected component of
the force acting along line OA.F=300 N
SOLUTION
Force and Unit Vector: The force vector Fand unit vector uOA must be determined
first. From Fig. a
159
2–138.
Determine the angle
u
between the two cables.
z
B
C
y
4 ft
6 ft
10 ft
10 ft
8 ft
uFAB 12 lb
SOLUTION
2–139.
Determine the projected component of the force
F = 12 lb acting in the direction of cable AC. Express the
result as a Cartesian vector.
z
B
C
y
4 ft
6 ft
10 ft
10 ft
8 ft
uFAB 12 lb
SOLUTION