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).

Cartesian Vector Form

Unit Vectors

Position Vector

Dot Product:

VECTORS in 3-D Space

BA

Cartesian Vector Form:

• Or using the unit vector eF:

• If

• Remember that

kFjFiFF zyxˆˆˆ

FFF e

:known then are ,, zyx

kjie zyxFˆcosˆcosˆcos

1e F

Unit Vector from Coordinates• If coordinates of position are given, e.g. (dx,dy,dz)

• Magnitude of vector d:

• Then:

kjie zyxF

ˆd

dˆd

dˆd

d

d

d

FFF e

2z

2y

2x dddd

Direction of vector F:

• Using Information of coordinates

d

dcos

d

dcos

d

dcos

Angles

1

1

1

zz

yy

xx

Activity#1: Analytical

(1) Find the Unit vector eF

(2) Express F in cartesian vector form.

Z).Y,(X,Position of sCoordinate and F

x

y

z

F=100N

d(2,-4,3

Dot Product:

• Define as:

• Dot Product of two Vectors = Scalar.

cosBA AB BA

A

B

Application of Dot Product

• Dot product of Unit Vectors:

• Dot Product of same Vector:

kji ˆ,ˆ,ˆ

00(1)(1)cos9ikkjji

1(1)(1)cos0kkjjiio

o

2z

2y

2x

22 AAAA0cosAAA o

Activity#2: Maple

• If position given: d1(3,-2.5,3.5)ft.

• Find: (1) Magnitude of distance:

(2) Unit vector 1e

1d

x

y

zd1(3,-2.5,3.5)

Activity#3: Maple

(1) Find the Unit vector eF

(2) Express F in cartesian vector form.

Z).Y,(X,Position of sCoordinate and F

x

y

z

F=100N

d(2,-4,3)

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:

0F 0Fx 0Fy