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: [pmath](matrix{2}{1}{x y})[/pmath], you can find the magnitude of the vectors usually by applying Pythagoras Theorem.
So magnitude of vectors = [pmath]sqrt{x^2+y^2}[/pmath]. 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, [pmath]vec{AB} = vec{AO} + vec{OB}[/pmath] 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:
[pmath]vec{AC} =k vec{BD}[/pmath] where k is a scalar factor.What this means is that [pmath]vec{AC}[/pmath] is // to [pmath]vec{BD}[/pmath] and the magnitude of [pmath]vec{AC}[/pmath] is k times that of [pmath]vec{BD}[/pmath]
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.
Ai Ling Ong
Hi, I'm Ai Ling Ong. I enjoy coaching students who have challenges with understanding and scoring in 'O' Level A-Maths and E-Maths. I develop Math strategies, sometimes ridiculous ideas to help students in understanding abstract concepts the fast and memorable way. I write this blog to share with you the stuff I teach in my class, the common mistakes my students made, the 'way' to think, analyze... If you have found this blog post useful, please share it with your friends. I will really appreciate it! :)
please i dont understand my math school papers is in 1 day and i only need to learn vectors and transformation please could u send me an e-mail giving details about these topics ur help would really be appreciated. Please the paper is tmr
I'm a first year Maths student in Myanmar. I interest GCE'o' Maths so much.
thank you very much for your explanation! it really helped.
i will appreciate if you can tell me if there is another method of finding k and P.
thanks in advance.