Page 68 - Dynamics of Mechanical Systems

0593_C02_fm Page 49 Monday, May 6, 2002 1:46 PM

Review of Vector Algebra 49

a. Determine the magnitudes of A and B.
b. Find the angle between A and B.

P2.6.5: Let vectors A and B be expressed in terms of mutually perpendicular unit vectors as:

A = 4 n + n − 5 n and B = 2 n + B n + n
1 2 3 1 y 2 3

Find B so that the angle between A and B is 90˚.
y
P2.6.6: See Figure P2.6.6. Let the vector V be expressed in terms of mutually perpendicular
unit vectors n , n , and n , as:
z
y
x
V = 3 n + 4 n − 2 n
x y z
Let the line L pass through points A and B where the coordinates of A and B are as shown.
Find the projection of V along L.

Z

n
z
L
B(1,7,3)
A(2,1,2)
V
O
Y
n
y
FIGURE P2.6.6
A vector V and a line L. X n x

P2.6.7: A force F is expressed in terms of mutually perpendicular unit vectors n , n , and
y
x
n as:
z
F =− 4 n + 2 n − 7 n lb
y
z
x
If F moves a particle P from point A (1, –2, 4) to point B (–3, 4, –5), find the projection of
F along the line AB, where the coordinates (in feet) of A and B are referred to an X, Y, Z
Cartesian system and where n , n , and n are parallel to X, Y, and Z.
x
y
z
P2.6.8: See Problem P2.6.7. Let the work W done by F be defined as the product of the
projection of F along AB and distance between A and B. Find W.

Section 2.7 Vector Multiplication: Vector Product
P2.7.1: Consider the vectors A and B shown in Figure P2.7.1. Using Eq. (2.7.1), determine
the magnitude of the vector product A × B.

a. If A and B are in the X–Y plane, what is the direction of A × B?
b. What is the direction of B × A?