1. VECTORS in 3-D Space Vector Decomposition Addition of Vectors:
Fx, Fy, Fz
Addition of Vectors:
Cartesian Vector Form:
Unit Vectors:

2. Vectors in 3-D Space: Vector Components Fx = |F| cos x
Fy = |F| cos y
Fz = |F| cos z z F Fz y Fy Fx x

3. Cartesian Representation
Cartesian Vector Form:
Vector Components
Fx = |F| cos x
Fy = |F| cos y
Fz = |F| cos z
Magnitude
Directional Cosines:
Trigonometry Identity
cos x =
cos y =
cos z=
cos2x + cos2y + cos2 z = 1

4. Cartesian Representation
Cartesian Form:

5. Different Problems
Case 1:

6. Activity #1:
Write the vectors F1, F2 in cartesian vector: (just write equation without doing calculations).
Using Maple add vectors F1, F2 to find R.
Using Maple Find Magnitude of R

7. Unit Vector in Direction of F:
Cartesian Vector Form
Unit Vector, eF , in Direction of F:
Dividing Above Eqn by its magnitude:
But, since we know:

8. Unit Vector So, a unit vector is given by a vector F:
Or by its directional cosines:
To find

9. Activity #2: For previous activity find using MAPLE
(a) Unit vector in direction of F: eF
(b) Magnitude of the Unit Vector: eF
(c) Angle of Resultant force R:

10. Unit Vector from Position
In some case the angles of a vector are not given, neither the components of force.
ONLY know: z
A(3,-4,5
F=10N y x

11. Activity #3 Solve Problem 2.81 using MAPLE.
Follow the example given in Class
Class of Prob. 2.80