Vectors
A vector is a quantity that has both a magnitude and a direction, written as a column or with arrows.
▶ Interact
Play with the controls to see the idea in action.
📘 Learn
A vector is a quantity that has both a magnitude and a direction, written as a column or with arrows.
- Add vectors by adding components
- A negative vector reverses direction
- Parallel vectors are multiples of each other
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Vectors?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Vectors. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Vectors in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Vectors gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Vectors in detail
A vector has both magnitude (size) and direction, unlike a scalar, which has size only. In 2D it is written as a column (x over y) or as a letter in bold, such as a, or as AB for the journey from A to B. The negative of a vector has the same length but opposite direction.
Vectors add by joining them head to tail and can be multiplied by a scalar to stretch them. Parallel vectors are scalar multiples of each other, which is used to prove that points lie on a straight line. Vectors describe forces, velocities and displacements in physics and navigation.
How the interactive helps you understand Vectors
Move the slope and y-intercept sliders. The line and its equation update, so you can see how the slope sets the steepness and the intercept sets where the line crosses the y-axis.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Vectors.
Real-life uses and examples
- Check a homework answer about Vectors by estimating first, then working it out step by step.
- Use Vectors when comparing prices, discounts or recipe quantities in everyday life.
- Explain Vectors to a friend with a simple picture, such as a row of tiles or a bag of sweets.
Common mistakes to avoid
- Memorising the steps for Vectors without checking why they work.
- Forgetting units, signs or brackets when you apply Vectors.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Vectors
What is Vectors?
A vector is a quantity that has both a magnitude and a direction, written as a column or with arrows.
What are the most important points about Vectors?
The main points are: Add vectors by adding components; A negative vector reverses direction; Parallel vectors are multiples of each other.
Why is Vectors useful?
Understanding Vectors gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Vectors?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Vectors?
Related topics in Mathematics include Tree Diagrams and Combined Events, Mean, Median and Mode, Bar Charts and Pictograms.