Page 65 - Dynamics of Mechanical Systems

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

46 Dynamics of Mechanical Systems

Y A |A| = 10 N
j |B| = 15 N
30°
B

45°

X
FIGURE P2.4.1
Vectors A and B and a unit vector. i

P2.4.3: Given the unit vectors i and j and the vectors A and B as shown in Figure P2.4.3,
let the magnitudes of A and B be 15 lb and 26 lb, respectively. Express A and B in terms
of i and j.

Y
j
A
B
3 5
4 12
X
FIGURE P2.4.3
Vectors A and B and unit vectors. i
P2.4.4: See Problem 2.4.3. Let C be the resultant of A and B.

a. Express C in terms of i and j.
b. Find the magnitude of C.

P2.4.5: Given the Cartesian coordinate system as shown in Figure P2.4.5, let A, B, and C
be points in space as shown. Let n , n , and n be unit vectors parallel to X, Y, and Z.
z
x
y
a. Express the position vectors AB, BC, and CA in terms of n , n , and n .
z
x
y
b. Find unit vectors parallel to AB, BC, and CA.
Z
n z
A(3,-1,4)
B(1,3,3)

O
Y
n
y
FIGURE P2.4.5 C(4,6,-1)
A Cartesian coordinate system with points
A, B, and C. X n x

P2.4.6: See Problem P2.4.5. Let R be the resultant of AB, BC, and CA. Express R in terms
of n , n , and n .
z
y
x