Column Vectors Worksheet

Column vectors at a glance

Column vectors describe a movement. The top number of a column vector is the x component – it tells us where to move in the x direction (right and left). The bottom number is the y component – it tells us where to move in the y direction (up and down). For example, the column vector of 3 on top of  negative 4 in large round brackets describes a movement of 3 in the positive x direction (right) and 4 in the negative y direction (down). 

A column vector can be multiplied by a scalar. When multiplying a vector by a scalar, we multiply both components of the vector by the scalar. Two vectors are parallel if one is a scalar multiple of the other. Multiplying a vector by -1 would give a vector of the same length but in the opposite direction. 

We can perform vector addition and subtraction with column vectors. To do this, we add or subtract the x components of each vector and then add or subtract the y components. 

The magnitude of a vector is its length. The magnitude of a column vector can be found using Pythagoras’ Theorem. By drawing lines representing the x component and y component of the vector, we can construct a right angle triangle. The magnitude is the length of the hypotenuse of the triangle formed. 

Looking forward, students can then progress to additional geometry worksheets, for example the vector problems worksheet, the transformations worksheet, or the Pythagoras’ Theorem worksheet.

For more teaching and learning support on Geometry our GCSE maths lessons provide step by step support for all GCSE maths concepts.