3. Section 3.1:
Vectors and their Properties
Vector
Magnitude & Direction
i.e. ρ
v - instantaneous velocity
r
a - instantaneous acceleration
Scalar
Magnitude only
4. Equality of Two Vectors
Two vectors are equal if
they have the same
magnitude and same
direction
5. Vector Addition
ρ r
ρ r r
Given two vectors A & B ,
what is R = A + B ?
ρ
B
ρ
A
6. Graphical Techniques of Vector
Addition
ρ
R ρ
“Tip-to-Tail Method” B
ρ
Two vectors can be added by A
placing the tail of the 2nd on
the tip of the 1st ρ
A
ρ
B ρ
R
7. Multiplying a Vector by a Scalar
ρ r
Given s , what is 3s ?
r r r r ρ
3s = s + s + s ρ s
ρ s
s r
3s
8. Graphical Techniques of Vector
Addition
What about subtraction?
ρ r r r
A - B = A + (- B)
ρ ρ
A B
ρ r ρ
A- B −B
9. Quiz Question 1
The vector c in the diagram is equal to
ρ r ρ
1. a + b
ρ r ρ c
2. b + a b
ρ r
ρ r
3. a - b ρ
4. b - a a
5. None of these
10. Quiz Question 2
ρ r
The magnitudes of two vectors a & b are 12 units
and 8 units, respectively. What are the largest and
smallest possibleρvaluesrfor the magnitude of the
r
resultant vector R = a + b ?
3. 14.4 and 4
4. 12 and 8
5. 20 and 4
6. None of these
11. Section 3.2:
Components of a Vector
ρ r r
A = Ax + Ay
Where Ax and Ay are the ρ
components of the vector A
Ax = Acosq
Ay = Asinq
12. Components of a Vector
ρ r r
A = Ax + Ay
Notice also that…
A = Ax2 + Ay2
Ay
tanq =
Ax
13. Quiz Question 3
ρ r r
The angle between A = Ax + Ay where
Ax = 25 & Ay = 45 and the positive x
axis is:
p 29°
p 61°
p 151°
p 209°
p 241°
14. Addition by Vector Components
ρ r r
Given that…
a = ax + ay where ax = 3,ay = 2
r r r
b =rbx + by where bx =1,by = - 4
ρ
What is a+b?
Answer Algebraically & Graphically…
r r
What is | a + b | ?, θ ?
