Column Vectors Revision and worksheets

Column Vectors Revision and worksheets

GCSE 4 - 5AQAEdexcelOCRWJECFoundationAQA 2022Edexcel 2022OCR 2022WJEC 2022

Column Vectors

A vector is something that has both a magnitude and direction. On diagrams they are denoted by an arrow, where the length tells us the magnitude and the arrow tells us the direction.

Vectors are often split up into two parts, which we call components: An x component, which moves left or right, and a y component, which moves up or down.

Make sure you are happy with the following topics before continuing:

Level 4-5 GCSE AQA Edexcel OCR WJEC
Column Vectors Diagram

What are Column Vectors?

A column vector splits the x and the y direction up, with x on top and y on bottom.

\begin{pmatrix}x\\y \end{pmatrix}

e.g. the vector \mathbf{a} goes 3 spaces to the right and 2 spaces up, so would be expressed as \begin{pmatrix}3\\2 \end{pmatrix}.

Column Vectors Diagram
Level 4-5 GCSE AQA Edexcel OCR WJEC

Adding and subtracting column vectors.

To add/subtract column vectors, we add/subtract the x and y values separately.

\begin{pmatrix}a\\b \end{pmatrix} + \begin{pmatrix}c\\d \end{pmatrix} = \begin{pmatrix}a + c\\b + d \end{pmatrix}

For example:



Level 4-5 GCSE AQA Edexcel OCR WJEC

Multiplying Column Vectors.

To multiply a column vector by a number, we multiply both values in the vector by that number, e.g.


Level 4-5 GCSE AQA Edexcel OCR WJEC

Example Questions

Firstly, to multiply \mathbf{a} by 2, we must multiply both of its components by 2:




Then, to add this to \mathbf{b}, we must add the x values and y values separately. Doing so, we get the answer to be:



Firstly, to multiply \mathbf{a} by 3, we must multiply both of its components:




Then, in order subtract 2\mathbf{b}, we must first multiply \mathbf{b} by 2.




Thus the calculation is:


Firstly, to multiply \mathbf{b} by 2, we must multiply both of its components:




Then, we can add \mathbf{a}  and  2\mathbf{b}:




The final calculation is to subtract \mathbf{c}:


\mathbf{a}+2\mathbf{b}-\mathbf{c}=\begin{pmatrix}16\\-4\end{pmatrix}-\begin{pmatrix}2\\1\end{pmatrix} = \begin{pmatrix}14\\-5\end{pmatrix}

Related Topics


Coordinates and Ratios

Level 4-5Level 6-7KS3

Direct and Inverse Proportion

Level 4-5Level 6-7KS3

Worksheet and Example Questions

Site Logo

(NEW) Column Vectors Exam Style Questions - MMe

Level 4-5 GCSENewOfficial MME

You May Also Like...

GCSE Maths Revision Cards

Revise for your GCSE maths exam using the most comprehensive maths revision cards available. These GCSE Maths revision cards are relevant for all major exam boards including AQA, OCR, Edexcel and WJEC.

View Product

GCSE Maths Revision Guide

The MME GCSE maths revision guide covers the entire GCSE maths course with easy to understand examples, explanations and plenty of exam style questions. We also provide a separate answer book to make checking your answers easier!

From: £14.99
View Product