10/8 Do now
• The diagrams below represent two types motions.
One is constant motion, the other, accelerated
motion. Which one is constant motion and which
one is accelerated motion? Explain your answer.
A.
B.
Essay homework is due
Chapter 3 project – due Tuesday 10/15
Tonight’s Homework – read text book page 84-85
and write an essay to indicate:
1. How to distinguish between a scalar and a
vector?
2. How is a vector represented?
3. How to add and subtract vectors graphically?
4. What are some properties of vectors?
5. How to multiply or divide a vector by a scalar?
Be sure to include definitions of scalar, vector,
resultant, Use examples in your essay to clarify
ideas.
3-1 introduction to vectors
1. Distinguish between a scalar and a vector.
2. Add and subtract vectors using the graphical
method.
3. Multiply and divide vectors by scalars.
No post session after school today or tomorrow
• Vector: a physical quantity that has both a
magnitude and a direction. We use an arrow
above the symbol to represent a vector.

A
• Scalar: a physical quantity that has only a
magnitude but no direction.
A
Representing Vectors
• Vectors on paper are simply arrows
– Direction represented by the way the ARROW POINTS
– Magnitude represented by the ARROW LENGTH
• Examples of Vectors
– Displacement
– Velocity
– Acceleration
Equal vectors: same
magnitude
Same direction
Opposite vector: same
magnitude
opposite direction
Directions of Vector
Compass Point
The direction of a vector is often expressed as an angle of
rotation of the vector about its "tail" from east, west,
north, or south
20 meters at 10° south of west
34 meters at 42° east of north
N
W
0°
S
Directions of Vector
Reference Vector
Uses due EAST as the 0 degree reference,
all other angles are measured from that point
20 meters at 190°
34 meters at 48°
90°
0°
180°
270°
Reference vector
Changing Systems
• What is the reference vector angle for a vector
that points 50 degrees east of south?
270° + 50° = 320°
50°
• What is the reference vector angle for a vector
that points 20 degrees north of east?
20°
20°
Vector Diagrams
1. a scale is clearly listed
2. a vector arrow (with arrowhead) is
drawn in a specified direction. The
vector arrow has a head and a tail.
3. the magnitude of the vector is clearly
labeled.
head
tail
Vectors can be moved parallel to themselves in a diagram
What we can DO with vectors
demo
• ADD/SUBTRACT with a vector
– To produce a NEW VECTOR (RESULTANT)
• MULTIPLY/DIVIDE by a vector or a scalar
– To produce a NEW VECTOR or SCALAR
Vector Addition
• Two vectors can be added together to determine the
sum (or resultant).
The resultant is the
vector sum of two
or more vectors. It
is the result of
adding two or
more vectors
together
Two methods for adding vectors
A
A
+
B
=?
B
• Graphical method: using a scaled vector
diagram
– The head-to-tail method (tip to tail)
– Parallelogram method
• Mathematical method - Pythagorean theorem
and trigonometric methods
Vector addition: head-to-tail method
• A cart is pushed in two directions, as the result, the
cart will move in the resultant direction
+
A
+
=
B
=
C
(Resultant)

A
C
B
A

B
The resultant is from the first tail to the last head.
The head-to-tail method (triangle method of addition)
• Page 85.
Steps for adding vectors using head and tail method
1. Choose a scale and indicate it on a sheet of paper. The best
choice of scale is one that will result in a diagram that is as
large as possible, yet fits on the sheet of paper.
2. Pick a starting location and draw the first vector to scale in
the indicated direction. Label the magnitude and direction of
the scale on the diagram (e.g., SCALE: 1 cm = 20 m).
3. Starting from where the head of the first vector ends, draw the
second vector to scale in the indicated direction. Label the
magnitude and direction of this vector on the diagram.
4. Repeat steps 2 and 3 for all vectors that are to be added
5. Draw the resultant from the tail of the first vector to the
head of the last vector. Label this vector as Resultant or
simply R.
6. Using a ruler, measure the length of the resultant and
determine its magnitude by converting to real units using the
scale (4.4 cm x 20 m/1 cm = 88 m).
7. Measure the direction of the resultant using the reference
counterclockwise convention.
10/9 do now
• Add following vectors using head and tail method to
determine the resultant, use a ruler and a protractor.
1. 3 m east, and 4 m south.
2. 5 m north and 12 meters west.
3. 2 m east, 4 m north and 5 m west.
1.
2.
3.
4.
5.
6.
7.
Choose a scale and indicate it on a sheet of paper. The best choice of scale is one
that will result in a diagram that is as large as possible, yet fits on the sheet of paper.
Pick a starting location and draw the first vector to scale in the indicated direction.
Label the magnitude and direction of the scale on the diagram (e.g., SCALE: 1
cm = 20 m).
Starting from where the head of the first vector ends, draw the second vector to
scale in the indicated direction. Label the magnitude and direction of this vector on
the diagram.
Repeat steps 2 and 3 for all vectors that are to be added
Draw the resultant from the tail of the first vector to the head of the last vector,
with an arrow. Label this vector as Resultant or simply R.
Using a ruler, measure the length of the resultant and determine its magnitude by
converting to real units using the scale (4.4 cm x 20 m/1 cm = 88 m).
Measure the direction of the resultant using the reference counterclockwise
convention.
Essay homework is due
Chapter 3 project – due Tuesday 10/15
Tonight’s Homework – castle learning
What is A + B?
R
A
B
A
R
B
Parallelogram method
• A cart is pushed in two directions, as the result, the
cart will move in the resultant direction
A
C
B
Parallelogram vs. head-to-tail

A

A

B

A
2 heads
together

B

B
Parallelogram: tail and tail touching,
the resultant is the diagonal.
Head-to-tail: head and tail touching, the
resultant is from first tail to last head.
Practice – parallelogram method
• Add following vectors to determine the
resultant, use a ruler and a protractor.
1.3 m east, and 4 m south.
2.5 m north and 12 meters west.
Vector properties
• Vector can be moved parallel to themselves in a diagram.
 
A B

B

A
• Vectors can be added in any order (commutative and
   
associative)

A B  B  A

B

A
A
B
• To subtract a vector, add its opposite.

B

A
  

A  B  A  ( B)
• Multiplying or dividing vectors by scalars results in vectors with
different size, but same direction.
10/10 Do now: what is the title of this
animation:?
Vector subtraction
-
A
=
-
B
=
=
?
A
+
(- B )
+
vector addition vs. subtraction
A
B
Equilibrant
• The equilibrant vectors of A and B is the
opposite of the resultant of vectors A and B.
• Example:
B
A
B
A
Head to tail
R
A
B
R
Parallelogram
Do Now: What is 6 + 8 ?
Class work
• Page 87, section review #1-5
• Section review work sheet 3-1
• Page 113, #1-13
• Homework: castle learning
do now
• Write all you know all about vector
– Definition:
– Examples (3):
– Representation:
– Ways to add vectors graphically, show sketches to
illustrate your understanding
Do Now: What is 6 + 8 ?