E-Math: Parallel Vectors & Collinear


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.

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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! :)

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