Page 70 - Dynamics of Mechanical Systems

0593_C02_fm Page 51 Monday, May 6, 2002 1:46 PM

Review of Vector Algebra 51

P2.7.5: Let A and B be expressed in terms of mutually perpendicular unit vectors n , n ,
1
2
and n as:
3
A = 3 n − 6 n + 8 n
1 2 3
B = 4 n − n − 5 n
1 2 3

Find a unit vector perpendicular to A and B.
P2.7.6: See Figure P2.7.6. Let X, Y, and Z be mutually perpendicular coordinate axes, and
let A, B, and C be points with coordinates relative to X, Y, and Z as shown.

a. Form the position vectors AB, BC, and CA, and express the results in terms of
the unit vectors n , n , and n .
x
z
y
b. Evaluate the vector products AB × BC, BC × CA, and CA × AB.
c. Find a unit vector n perpendicular to the triangle ABC.
Z
B(3,7,5)
n A(1,1,4)
z

O C(2,5,1)
Y
n
FIGURE P2.7.6 y
A triangle ABC in an X, Y, Z reference
frame. X n x
P2.7.7: See Figure P2.7.7. Let LP and LQ be lines passing through points P , P and Q , Q 2
1
2
1
as shown. Let the coordinates of P , P , Q , and Q relative to the X, Y, Z system be as
1
2
2
1
shown. Find a unit vector n perpendicular to LP and LQ, and express the results in terms
of the unit vectors n , n , and n shown in Figure P2.7.7.
y
x
z
Z L
Q (-1,-2,7) P (0,6,4) P
2
1
n
z
Q (4,5,2)
2
P (3,-1,3)
1
L Q
Y
n
FIGURE P2.7.7 y
Lines LP and LQ in an X, Y, Z reference n
frame. X x
P2.7.8: See Figure P2.7.8. Let points P and Q have the coordinates (in feet) as shown. Let
L be a line passing through P and Q, and let F be a force acting along L. Let the magnitude
of F be 7 lb.