Page 69 - Dynamics of Mechanical Systems

0593_C02_fm Page 50 Monday, May 6, 2002 1:46 PM

50 Dynamics of Mechanical Systems

|A| = 45
Y
|B| = 30
B

30°
A
FIGURE P2.7.1
Vectors A and B in the X–Y plane. X

P2.7.2: See Problem P2.7.1. What is the magnitude of 6A × 2B?
P2.7.3: Consider the vectors A, B, and C shown in Figure P2.7.3. Let i, j, and k be mutually
perpendicular unit vectors as shown, with k being along the Z-axis.

a. Evaluate the sum B + C.
b. Determine the vector products A × B and A × C.
c. Use the results of (b) to determine the sum of A × B and A × C.
d. Use the results of (a) to determine the product A × (B + C). Compare the result
with that of (c).

Y |A| = 45
C |B| = 30
B |C| = 35
j
30°
30°
A
O
X
FIGURE P2.7.3 i
Vectors A, B, and C in the X–Y plane. k
P.2.7.4: Let n , n , and n be mutually perpendicular (dextral) unit vectors, and let vectors
1
2
3
A, B, and C be expressed in terms of n , n , and n as:
1
2
3
A = 6 n − n + n 3
1
2
B =−5 n + 4 n − 2 n 2
2
1
C = 3 n + 5 n − 7 n 3
2
1
a. Evaluate the sum B + C.
b. Use Eq. (2.7.24) to determine the vector products A × B and A × C.
c. Use the results of (b) to determine the sum of A × B and A × C.
d. Use the results of (a) to determine the product A × (B + C). Compare the result
with that of (c).