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.


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


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.


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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