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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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