What Are Vectors? 121

We, at least we

a made it in!

Try to remember

the minigolf

example while

wetalk about the

next few subjects.

Vectors can be

interpreted in four

dierent ways. Let

me give you a quick

walk-through of a

of them.

7

4

I' use the

1×2

matrix

(7, 4)

and the

2×1

matrix

to make things

simpler.

Okay.

1×n matrices and n×1 matrices

122 Chapter 5 Introduction to Vectors

The point (7, 4)

x

2

4

7

x

1

O

x

2

4

7

x

1

O

x

2

4

3

743

x

1

O

x

2

4

1

10

107

x

1

O

Interpretation 1

Interpretation 2

Interpretation 3

interpreted as a point in space.

7

4

(7, 4) and are sometimes

In other cases, (7, 4) and

7

4

are interpreted as the

“aow” from the origin

to the point

(7, 4).

(7, 4) and

7

4

can mean the

sum of several

aows equal

to

(7, 4).

And in yet

other cases,

What Are Vectors? 123

x

2

4

7

x

1

O

Interpretation 4

7

4

Finay, (7, 4) and can also

be interpreted as any of

the aows on my left, or

a of them at the same time!

Hang on a second.

I was with you until

that last one...

7

4

How could a

of them be

representations of

(7, 4)

and

when they start

in completely

dierent

places?

While they do start

in dierent places,

they're a the same in

that they go “sevento

the right and four up,”

right?

Yeah, I gue

that's true!

124 Chapter 5 Introduction to Vectors

Vectors are

kind of a

mysterious

concept, don't

you think?

We, they may

sm that way

atfirst.

but...

Once you've got the

basics down, you' be

able to aly them to

a sorts of interesting

problems.

For example,

they're frequently

used in physics to

describe dierent

types of forces.

Cl!

Puing force

Gravitational force

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