How to Add Simple Vectors

Back to Maths Grade 9/10

This is a simple math and physics tutorial aimed at middle to high schoolers (grades 9 and 10) detailing how to add simple vectors.

What do we mean by simple vectors?

Any two vectors that are both horizontal, or both vertical (like the two examples below).

More complicated vectors (such as those below) will be covered in future tutorials.

How do we add simple vectors?

There are a four steps involved in adding simple vectors:

  1. Do a rough drawing of the circumstance / scenario, and include all of the vectors.
  2. Attribute positive and negative signs to directions.
  3. Do the simple arithmetic.
  4. Make sure that your result has both magnitude and direction (i.e. the answer should be a vector too!).

The video above covers conventions for attributing positive and negative signs to vectors, as well as three examples of working through theses steps. We'll work through the following example in this written tutorial:
Mr J decided to walk to the shops from his house. He had gone 20 meters to the west when he thought he had forgotten his wallet at home. He turned around, and walked 15 meters east when he realised that he had his wallet in his pocket. What was his final displacement?

Step 1

Below is our rough drawing of the scenarios, including all of the vectors.

Step 2

Assign positive and negative signs. It doesn't matter which way you choose to be positive or negative, so long as:
a) north and south are opposite to one another, and west and east are opposite to one another;
b) you're consistent; and
c) you're clear in your test answers what your positive or negative sign means.

You may find it easiest and best to follow the normal convention : any vectors pointing in a northerly or easterly direction are positive; any vectors pointing in a southerly or westerly direction are negative(Hover over the below compass ).

Let's assign these signs to our vectors.

Step 3

Do the simple algebra - you'll probably find keeping the arrows in your work will help you to remember step 4.

Step 4

Make sure that your result is a vector: Mr P's final displacement is 5 meters west of his house.

Exercise Worksheet

If you'd like to practice your simple vector calculations, check out this FREE worksheet here: There are five colourful and engaging exercises to work through to consolidate and test your understanding - plus there are answers for you to check your work against.