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Announcements:. Important Read before class HMK will be assigned in class NO LATE HMK ALLOW Due date next class Use Cartesian Components: F x , F y , F z Discuss Problems Prob. 2.28 and Prob. 2.56 Maple has UNIX complex (case sensitive). VECTORS in 3-D Space. Cartesian Vector Form

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announcements
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
VECTORS in 3-D Space
  • Cartesian Vector Form
  • Unit Vectors
  • Position Vector
  • Dot Product:
cartesian vector form
Cartesian Vector Form:
  • Or using the unit vector eF:
  • If
  • Remember that
unit vector from coordinates
Unit Vector from Coordinates
  • If coordinates of position are given, e.g. (dx,dy,dz)
  • Magnitude of vector d:
  • Then:
direction of vector f
Direction of vector F:
  • Using Information of coordinates
activity 1 analytical
Activity#1: Analytical

(1) Find the Unit vector eF

(2) Express F in cartesian vector form.

z

d(2,-4,3

F=100N

y

x

dot product
Dot Product:
  • Define as:
  • Dot Product of two Vectors=Scalar.
application of dot product
Application of Dot Product
  • Dot product of Unit Vectors:
  • Dot Product of same Vector:
activity 2 maple
Activity#2: Maple
  • If position given: d1(3,-2.5,3.5)ft.
  • Find:

(1) Magnitude of distance:

(2) Unit vector

z

d1(3,-2.5,3.5)

y

x

activity 3 maple
Activity#3: Maple

(1) Find the Unit vector eF

(2) Express F in cartesian vector form.

z

d(2,-4,3)

F=100N

y

x

discuss problem 2 80
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
Final Period
  • Quiz #1: Vectors
  • Chapter #3: Statics of Particles
    • Free Body Diagram: FBD
    • Equilibrium Eqns:
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