Introduction to vectors - Vectors

Introduction to vectors

The notion of vectors can be easily found in our daily surroundings – from airplane navigation to trajectories of balls during a sports game, to movements of a character you maneuver in your video games. In this section, we will learn about the graphical, and mathematical representation of a vector, as well as how to distinguish the differences between a scalar quantity and a vector quantity.

Related Concepts
Complex numbers and complex planes

Lessons

Notes:

Vector Quantity: a quantity having (positive) magnitude and (one) direction
Scalar Quantity: a quantity having only magnitude but not direction
Two – Dimensional Vectors:

2.
For the following vectors, express them in component form, matrix form, and rectangular form
3.
For the following vectors, express them in component form, matrix form, and rectangular form

Introduction to vectors

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

Get Started Now

Try reviewing these fundamentals first

GeometryCartesian plane

GeometryDraw on coordinate planes

Nope, got it.

Play next lesson

Nope, got it.

Play next lesson

That's the last lesson

Go to next topic

Still don't get it?

Nope, I got it.

Still don't get it?

Review these basic concepts…

Cartesian plane

Draw on coordinate planes

Nope, I got it.

Play next lesson or Practice this topic

Start now and get better math marks!

Keep exploring StudyPug

Start now and get better math marks!

Keep exploring StudyPug

Intro Lesson

Selected

Lesson: 1

Lesson: 2a

Lesson: 2b

Lesson: 2c

Lesson: 2d

Lesson: 3a

Lesson: 3b

Lesson: 3c

Intro

Learn

Practice

Do better in math today

Don't just watch, practice makes perfect

Do better in math today

Don't just watch, practice makes perfect

Lessons

Notes:

Vector Quantity: a quantity having (positive) magnitude and (one) direction Scalar Quantity: a quantity having only magnitude but not direction Two – Dimensional Vectors:

Intro Lesson

1.

Which of the following is/are a vector? i) 505050 miles per hour north ii) 40km/s2\sqrt{40 } km/s^2 40​km/s2 iii) −43.1∘C -43.1^{\circ} C −43.1∘C iv) 5641ft35641\; ft^3 5641ft3 v) 323232 Newton at 98∘98^{\circ} 98∘ west of north

2.

For the following vectors, express them in component form, matrix form, and rectangular form

a)

p⃗ \vec{p} p​

b)

q⃗ \vec{q} q​

c)

v⃗ \vec{v} v

d)

w⃗ \vec{w} w

3.

For the following vectors, express them in component form, matrix form, and rectangular form

a)

v⃗ \vec{v} v

b)

w⃗ \vec{w} w

c)

r⃗ \vec{r} r

Introduction to vectors

Don't just watch, practice makes perfect.

We have over 1850 practice questions in Algebra for you to master.

Geometry
Cartesian plane

Geometry
Draw on coordinate planes

or

Vector Quantity: a quantity having (positive) magnitude and (one) direction
Scalar Quantity: a quantity having only magnitude but not direction
Two – Dimensional Vectors:

Which of the following is/are a vector?
i)
$50$ miles per hour north
ii)
$\sqrt{40 } km/s^2$
iii)
$-43.1^{\circ} C$
iv) $5641\; ft^3$
v)
$32$ Newton at $98^{\circ}$ west of north

$\vec{p}$

$\vec{q}$

$\vec{v}$

$\vec{w}$

$\vec{v}$

$\vec{w}$

$\vec{r}$