What do you think?
Introduction to Adding Vectors
Objectives
• Name the parts of a vector arrow. • Correctly represent vectors
using vector arrows. • Add vectors graphically.
Representing Vectors using Vector Arrows
And also naming the parts of a vector arrow
How do we represent a vector?
We represent a vector using a VECTOR ARROW.
Why do you think we use an arrow rather
than something else?
What is VECTOR QUANTITY?
• It a quantity that is completely described by a magnitude and direction.
The Vector Arrow
Length represents the magnitude of the quantity.
Direction of the arrow represents the direction of the vector.
Adding Vectors
…with vectors which run along the same axes…
Let us try this.
5 km East +
4 km East
But the 5 km would not fit in the boundary of the paper.
Use a SCALE.
Tail to Tip Method
5 km East +
4 km East
5 km East + 4 km East
5 km East 4 km East R = 9 km East
5 km East + 4 km West
5 km East 4 km West
R = 1 km East
4 km East + 5 km West
4 km East 5 km West
R = 1 km West
You try this.
90.0 km, North +
72.0 km, South
Adding Vectors
…with vectors that are along different axes…
How about…
4 m/s, North +
3 m/s, East
4 m/s, North + 3 m/s, East
4 m
/s, N
orth
3 m/s, East
5 m/s,
?
4 m/s, North + 3 m/s, East
4 m/s, North + 3 m/s, East
4 m/s, North + 3 m/s, East
4 m/s, North + 3 m/s, East
4 m/s, North + 3 m/s, East
4 m
/s, N
orth
3 m/s, East
5 m/s,
36.9
o
5 m/s,
36.9
o
Construct this Vector.
5 m/s, 36.9o
Construct this Vector.
7.00 m/s, 15.0o
Naming Vectors
Naming them in Three Ways
4 m/s, North + 3 m/s, East
4 m/s, North + 3 m/s, East
4 m/s, North + 3 m/s, East
4 m
/s, N
orth
3 m/s, East
5 m/s,
36.9
o36.9o
The magnitude of this vector is 55 Newtons. Name this vector.
Determine the measures of angles.
Example
θ1
θ2
55.0 m, 35.0o east of north
Exercise
Number 1
θ1
θ2θ3
55.0 m, 35.0o West of North
Exercise
Number 2
θ1
θ2
θ3
10.0 N, South 65.0o West
Exercise
Number 3
θ1
θ2
θ3
50.0 m/s 300.0o
Name that Vector.
Example
θ1
θ2
55.0 m, 35.0o east of north Use methods 2 and 3.
Exercise
Number 4
θ1
θ2θ3
55.0 m, 35.0o West of NorthUse methods 2 and 3.
Exercise
Number 5
θ1
θ2
θ3
10.0 N, South 65.0o WestUse methods 1 and 3.
Exercise
Number 6
θ1
θ2
θ3
50.0 m/s 300.0o
Use methods 1 and 2.
End of Part