Tag Archive: parallel vectors

E-Math: Vectors – Explain why 3 points are on the same line

Written on September 7, 2010 by Ai Ling in E-Maths, Video Learning
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3 points on the same line has a term called ‘Collinear’. Are you at a loss of how to go about explaining why ABC is a straight line, why ABC is on the same line, why ABC is collinear?

They all meant the same thing. Here’s the template you can use everything you need to explain why ABC is a straight line in a vectors question:

Vectors-StraightLine_Page_05

To have a better understanding, it is best that you know that what’s the significance of scalar multiplication of vectors, I know it’s like ‘eeeeeeek’ but what it really means is as followed: (Not as bad as you thought)

Vectors-StraightLine_Page_02

Here’s the video for step by step:

http://www.youtube.com/watch?v=2QLfqtgWMZw

Note there’s a bonus question at the end of the video. Try it and leave me your answer on the comments section.

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E-Math: Parallel Vectors & Collinear

Written on March 20, 2010 by Ai Ling in E-Maths
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How to tell if 2 vectors are //?

It’s easy if you’re given a diagram. What if a diagram isn’t provided? Then we need to look at relationship between the vectors.

As long as 2 vectors are expressed as scalar multiple of each other, the 2 vectors are //. What exactly do I mean? Look at the following example equations, they are examples of vectors // to each other.

This also means if you’re able to establish such relationship between 2 vectors, you can prove that the vectors are // to each other.

parallel-vectors

Very often, question will ask you to explain why A, B and C lie on a straight line. (Look at Example 3)

The term to describe 3 points on the line is known as Collinear.

3 Points to show Collinear

  1. Establish a relationship between the 2 vectors
  2. Conclude that the 2 vectors are // to each other
  3. Common point is present

show-collinear

We can even draw a diagram to represent the two vectors. Since the relationship between the 2 vectors has a negative sign, it means that vectors AB and AC are in opposite direction. Vector AC is also twice of vector AB.

collinear

Do you have other ways to prove 3 points are collinear? I would love to hear from you.

Do you know that if you are asked to prove 2 vectors are //? A similar approach can also be used.

Follow me on twitter if you like to have more ‘O’ Level Math Tips.

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

Written on March 12, 2009 by Ai Ling in E-Maths, Reader Question, Video Learning
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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: (matrix{2}{1}{x y}), you can find the magnitude of the vectors usually by applying Pythagoras Theorem.

So magnitude of vectors = sqrt{x^2+y^2}. 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, vec{AB} = vec{AO} + vec{OB} 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:

vec{AC} =k vec{BD} where k is a scalar factor.What this means is that vec{AC} is // to vec{BD} and the magnitude of vec{AC} is k times that of vec{BD}

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.

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