Title: In this chapter we will learn about vectors, properties, addition, components of vectors and multipl
1Chapter 3 Vectors
Things to ask the class Have you all checked
your WebCT account? Do the Quiz, participate in
the discussion and learn from the applets!
- In this chapter we will learn about vectors,
(properties, addition, components of vectors and
multiplying)
2Vectors Magnitude and direction Scalars
Only Magnitude A scalar quantity has a single
value with an appropriate unit and has no
direction.
Examples for each Vectors Scalars
Motion of a particle from A to B along an
arbitrary path (dotted line). Displacement is a
vector
3- Vectors
- Represented by arrows (example displacement).
- Tip points away from the starting point.
- Length of the arrow represents the magnitude
- In text a vector is often represented in bold
face (A) or by an arrow over the letter. - In text Magnitude is written as A or
This four vectors are equal because they have the
same magnitude and same length
4Adding vectors
Graphical method (triangle method)
Draw vector A. Draw vector B starting at the
tip of vector A. The resultant vector R A B
is drawn from the tail of A to the tip of B.
5Adding several vectors together.
Resultant vector RABCD is drawn from the
tail of the first vector to the tip of the last
vector.
6Commutative Law of vector addition
A B B A
(Parallelogram rule of addition)
7Associative Law of vector addition
A(BC) (AB)C
The order in which vectors are added together
does not matter.
8Negative of a vector. The vectors A and A have
the same magnitude but opposite directions. A
(-A) 0
A
-A
9Subtracting vectors
A - B A (-B)
10Multiplying a vector by a scalar
The product mA is a vector that has the same
direction as A and magnitude mA. The product
mA is a vector that has the opposite direction
of A and magnitude mA.
Examples 5A -1/3A
11Components of a vector
The x- and y-components of a vector
The magnitude of a vector
The angle q between vector and x-axis
12The signs of the components Ax and Ay depend on
the angle q and they can be positive or negative.
(Examples)
13Unit vectors
- A unit vector is a dimensionless vector having
a magnitude 1. - Unit vectors are used to indicate a direction.
- i, j, k represent unit vectors along the x-, y-
and z- direction - i, j, k form a right-handed coordinate system
14The unit vector notation for the vector A is OR
in even better shorthand notation
15Adding Vectors by Components
We want to calculate R A B From diagram R
(Axi Ayj) (Bxi Byj) R (Ax Bx)i
(Ay By)j
Rx Ax Bx Ry Ay By
The components of R
16Adding Vectors by Components
The magnitude of a R
The angle q between vector R and x-axis
17Checkpoint 3 (page 45)
What are the signs of x components of d1 and
d2? What are the sign of the y components of d1
and d2? What are the signs of the x and y
components of d1d2
18Sample Problem 3-4
19Vectors and the Laws of Physics
This section will be left as a reading assignment
for the student.
20Multiplying a vector by another vector Two types
21(No Transcript)