Announcements:
• Important Read before class
• HMK will be assigned in class
• NO LATE HMK ALLOW
– Due date next class
• Use Cartesian Components: Fx, Fy, Fz
• Discuss Problems
– Prob. 2.28 and Prob. 2.56
• Maple has UNIX complex (case sensitive).
VECTORS in 3-D Space
 Cartesian Vector Form
 Unit Vectors
 Position Vector
 Dot Product: A  B
Cartesian Vector Form:
F  Fxiˆ  Fy ˆj  Fz kˆ
• Or using the unit vector eF:
F  F eF
• If  x , y , z are known then :
eF  cos xiˆ  cos y ˆj  cos z kˆ
• Remember that
eF  1
Unit Vector from Coordinates
• If coordinates of position are given, e.g. (dx,dy,dz)
d dx ˆ dy ˆ dz ˆ
eF   i 
j k
d
d
d
d
• Magnitude of vector d:
d  d d d
2
x
• Then:
F  F eF
2
y
2
z
Direction of vector F:
• Using Information of coordinates
Angles
dx 

d




 x  cos 1 
 y  cos
 z  cos
1
1
d y


 d




dz 


d




Activity#1: Analytical
(1) Find the Unit vector eF
(2) Express F in cartesian vector form.
F and Coordinate s of Position (X, Y, Z).
d(2,-4,3
z
F=100N
y
x
Dot Product:
• Define as:
A  B  B  A  A B cos
A

B
• Dot Product of two Vectors = Scalar.
Application of Dot Product
• Dot product of Unit Vectors: iˆ, ˆj , kˆ
î  î  ĵ  ĵ  k̂  k̂  (1)(1)cos0 o  1
î  ĵ  ĵ  k̂  k̂  î  (1)(1)cos9 0o  0
• Dot Product of same Vector:
A  A  A 2 cos 0o  A 2  A 2x  A 2y  A 2z
Activity#2: Maple
• If position given: d1(3,-2.5,3.5)ft.
• Find:
(1) Magnitude of distance: d1
(2) Unit vector e1
z
d1(3,-2.5,3.5)
y
x
Activity#3: Maple
(1) Find the Unit vector eF
(2) Express F in cartesian vector form.
F and Coordinate s of Position (X, Y, Z).
d(2,-4,3)
z
F=100N
y
x
Discuss Problem 2.80
• Discuss Analytical Approach
– Position Vector:
– Unit Vector from position vector
– Resultant Force
• Show Maple Solution
• Problem 2.81 solved same way
Final Period
• Quiz #1: Vectors
• Chapter #3: Statics of Particles
– Free Body Diagram: FBD
– Equilibrium Eqns:
F  0
F
x
0
F
y
0