What are 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) describing what vector and scalar measurements are, with examples and complementary exercises below.

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Written Tutorial

A vector is a measurement, but not all measurements are vectors. Measurements can be scalar or vector. In order to understand what vector measurements are, let's first have a look at what scalar measurements are.

What are scalar measurements?

A scalar measurement can be represented with a number alone (with relevant units). It describes a quantity, magnitude or size of a measurement alone. Temperature is a good example of a scalar measurement: when you report it, you only report a number with its relevant unit e.g. 25 degrees Celsius, 77 degrees Farenheit or 298 degrees Kelvin.

Another good example of a scalar measurement is mass; it can be expressed with a number and unit alone e.g. 100 kg.

What are vector measurements?

Vectors are a form of measurement that gives you both magnitude (size or quantity) and direction. Velocity is a good example of a vector measurement. It is not to be confused with speed, which is scalar.

Let's take the below person as an example. Their speed is 3 m/s <-- we know this is a scalar measurement because it only tells you how fast the person is running, not what direction they're running in. By contrast, their velocity will report their speed and the direction they're travelling in --> 3m/s to the East or 3 m/s to the right (either is correct). You can also use an arrow to indicate direction (hover your mouse over the image below for an example).

Why are vectors useful?

Vectors are useful because we can add them together in ways that we cannot add scalar measurements. For example if two forces are acting on a car, we can tell what the overall force is, and if there will be any movement.

You can learn how to add simple vectors here.

What are some other vector measurements?

Complementary Exercises

Below are some complementary exercises for you to work through in your own time to consolidate your understanding. You can download the document here:

Make notes

Want to make notes as you follow along to the above video? Click on this image to download the document: