Page 67 - Dynamics of Mechanical Systems

0593_C02_fm Page 48 Monday, May 6, 2002 1:46 PM

48 Dynamics of Mechanical Systems

a. Construct the position vectors OP, OQ, and PQ and express the results in terms
of n , n , and n .
x
z
y
b. Determine the distance between P and Q if the coordinates are expressed in
meters.
c. Find the angles between OP and the X-, Y-, and Z-axes.
d. Find the angles between OQ and the X-, Y-, and Z-axes.
e. Find the angles between PQ and the X-, Y-, and Z-axes.

Z P(0.5,1,3)

n
z
Q(2,5,2)

O
Y
n y
FIGURE P2.4.9
A Cartesian coordinate system with
points P and Q. X n x

Section 2.5 Angle Between Two Vectors
P2.5.1: From the definition in Section 2.5, what is the angle between two parallel vectors
with the same sense? What is the angle if the vectors have opposite sense? What is the
angle between a vector and itself?

Section 2.6 Vector Multiplication: Scalar Product
P.2.6.1: Consider the vectors A and B shown in Figure P2.6.1. Let the magnitudes of A
and B be 8 and 5, respectively. Evaluate the scalar product A · B.

|A| = 8
B |B| = 5
n
2
120°
FIGURE P2.6.1 A
Vectors A and B. n 1

P2.6.2: See Problem P2.6.1 and Figure P2.6.1. Express A and B in terms of the unit vectors
n and n as shown in the figure. Use Eq. (2.6.2) to evaluate A · B.
1
2
P2.6.3: See Problems P2.6.1 and P2.6.2. Let C be the resultant of A and B. Find the
magnitude of C.
P2.6.4: Let n , n , and n be mutually perpendicular unit vectors. Let vectors A and B be
3
2
1
expressed in terms of n , n , and n as:
2
1
3
A = −3 n + 5 n + 6 n and B = 4 n − 2 n + 7 n
1 2 3 1 2 3