Up Learn – A Level maths (edexcel) – 3D Vectors

Vector Diagrams: Summary

Here’s a summary of everything you need to know about vector diagrams


A*/A guaranteed or your money back

Yes, really. Find out more about our A*/A Guarantee below.

More information

Want to see the whole course?

No payment info required!

Up Learn – A Level maths (edexcel)


Here’s a reminder of the key points you should know about 3D vectors.

We can use vectors to describe movements in 2D space…

… but also movements in 3D space.

Just like 2D vectors, 3D vectors have a magnitude… and a direction.

And we can give vectors names.

We can represent them using point to point notation… [BA]

… or column vector notation by adding a third value… [(2 5 3) and then pulse the 3]

… or unit vector notation by adding this third unit vector, k. [2i + 5j + 3k and then pulse the 3k.]

To describe the position of a point, we can use coordinates… 

Or we can use a position vector instead.

Next, adding 3D vectors works just like adding 2D vectors.

Here’s what it looks like when we add two vectors in column vector notation.

And here’s what it looks like in unit vector form.

Here’s what it looks like when we multiply by a scalar in column vector notation…

… and in unit vector form.

If two vectors are multiples of one another, that means they’re parallel.

Next, we can find the magnitude of a 3D vector using 3D pythagoras.

And to find the distance between two points, we can either use this formula…

Or take the position vector for each point…

… subtract one from the other…

… and then find the magnitude of that new vector.

Finally, if you’re given a vector and asked to find the unit vector that points in the same direction…

Divide the original vector…by its magnitude.


Every course includes


Interactive Video Lessons

Video content that keeps you engaged and regular activities that keep you from losing focus


Detailed Quizzes

Technical, Memorisation and Mastery quizzes gradually build up your knowledge and understanding


Exclusive Practice Papers

Written by real examiners exclusively for Up Learn in order to give you additional confidence when preparing for exams


Progress Tracker to A*

Bespoke assessment and practice questions to chart your grade gains as you progress through your A Level Maths revision