E-Math: Introduction to Vectors

alwaysLovely — Tue, 12 Jan 2010 03:36:12 +0000

In Secondary 4, students are going to learn this chapter ‘Vectors’. Some love it, most hate it.

In today post, I’m going to share some basic concepts on Vectors.

What is a vector?

A vector is a quantity that has direction and magnitude. Common examples of vector include velocity, acceleration, displacement and force.

The opposite of vector is scalar, a quantity that has only magnitude. Examples include time, speed, distance and mass.

As you see, vector is closely associated with physics!

How do we represent a vector?

vector

Since vector involves magnitude and direction, there will always be an arrow indicting the direction. We call this vector

Vectors can be expressed in a column format called column vector. For this example, which means, starting from point A, 3 units to right and 1 unit up. It is similar to our coordinate system 3 units along x axis and 1 unit along y axis. In general, moving right and up have positive sign while moving left and down have negative sign.

In general:

How to find magnitude of a vector?

Using the same example,to find magnitude of , we use Pythagoras’s Theorem. (Refer to diagram above)

Magnitude of can be written as .

I hope you have understood the basic concepts of vectors. In future post, I’m going to write more about the application of vectors.Related Articles:

[Video]E-Math: Basics of Vectors (Plus: Video Solution of an Exam Question)

alwaysLovely — Thu, 12 Mar 2009 04:10:08 +0000

Vector is a nightmare for some students especially if you do not like Physics. But for O level Elementary Mathematics, the few concepts are still quite straightforward to grasp if you follow through step by step.

In this post, I am going to discuss the Basics of Vectors which include:

Finding magnitude of vectors
How to find vectors
Parallel vectors & its significance

This is the exam question used for illustration.

|Magnitude| of vectors

When vectors are given in column vector form: , you can find the magnitude of the vectors usually by applying Pythagoras Theorem.

So magnitude of vectors = . If you do not wish to remember this, you can always draw a diagram in 5 seconds to be able to find the magnitude of any vectors. (This is shown in the video below)

How to find vectors

Finding vectors is just like deciding an alternate route for your journey. You would want to take note of the start point and the end point. For example, My starting point is A, transition point is O and the end point is B.

Hint: When diagram is given, refer to diagram for help to plan the ‘alternate’ route. Otherwise, consider the points given in the question.Sometimes, 3 or more vectors can be involved.

Parallel Vectors

We can tell that 2 vectors are // to each other when they are expressed in this relationship:

where k is a scalar factor.What this means is that is // to and the magnitude of is k times that of

We discuss about // vectors in parallelograms and trapeziums too!

Hint: Parallel vectors have same ‘gradient’.

This is the question which I use to illustrate the 3 points above:

How did you find vectors so far? Is it easy to understand or you do not seem to know anything? Leave me your comments. I would love to hear from you!

In the next post, I will be discussing Finding Ratio of Areas in Vectors & the Strategies Involved. Related Articles:

singaporeolevelmaths » magnitude of vectors

E-Math: Introduction to Vectors

What is a vector?

How do we represent a vector?

How to find magnitude of a vector?

[Video]E-Math: Basics of Vectors (Plus: Video Solution of an Exam Question)