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