1. Physics Vectors
Javid

2. Scalars and Vectors Temperature = Scalar
Quantity is specified by a single number giving its magnitude.
Velocity = Vector
Quantity is specified by three numbers that give
its magnitude and direction
(or its components in three perpendicular directions).

3. Properties of Vectors
Two vectors are equal if they have the same magnitude and direction.

4. Adding Vectors

5. Subtracting Vectors

6. Combining Vectors

7. Using the Tip-to-Tail Rule

8. Question to think about
Question: Which vector shows the sum of A1 + A2 + A3 ?

9. Multiplication by a Scalar

10. Coordinate Systems and Vector Components
Determining the Components of a Vector
The absolute value |Ax| of the x-component Ax is the magnitude of the component vector .
The sign of Ax is positive if points in the positive x-direction, negative if points in the negative x-direction.
The y- and z-components, Ay and Az, are determined similarly.
Knight’s Terminology:
The “x-component” Ax is a scalar.
The “component vector” is a vector that always points along the x axis.
The “vector” is , and it can point in any direction.

11. Determining Components

12. Cartesian and Polar Coordinate Representations

13. Unit Vectors
Example:

14. Working with Vectors ^ A = 100 i m
B = (-200 Cos 450 i Cos 450 j ) m = (-141 i j ) m ^ ^ ^ ^
C = A + B = (100 i m) + (-141 i j ) m
= (-41 i j ) m ^ ^ ^ ^
C = [Cx2 + Cy2]½ = [(-41 m)2 + (141 m)2]½ = 147 m
q = Tan-1[Cy/|Cx|] = Tan-1[141/41] = 740
Note: Tan-1 Þ ATan = arc-tangent = the angle whose tangent is …

15. Tilted Axes
Cx = C Cos q Cy = C Sin q

16. Arbitrary Directions

17. Perpendicular to a Surface

18. Multiplying Vectors* Given two vectors: Dot Product (Scalar Product)
Cross Product (Vector Product)
A·B is B times the projection of A on B, or vice versa.
(determinant)

19. Spherical Coordinates*q R x y z f Ax Ay Az
0 £ q £ p
0 £ f £ 2p
Ax= R Sin q Cos f
Ay= R Sin q Sin f
Az= R Cos q
R = [Ax2 + Ay2 + Az2]½ = |A|
= Tan-1{[Ax2 + Ay2]½/Az}
f = Tan-1[Ay/Ax]

20. Cylindrical Coordinates*q r x y z Ax Ay Az
0 £ q £ 2p
Ax= r Cos q
Ay= r Sin q
Az= z
r = [Ax2 + Ay2]½
= Tan-1[Ay/Ax]
z = Az

21. Summary

22. Summary