GCSE Maths Practice: vectors

Column vectors are used to represent movement or displacement in two dimensions. Each vector has a top number representing horizontal movement (x-direction) and a bottom number representing vertical movement (y-direction). Subtracting vectors involves subtracting corresponding components: the top number minus the top number, and the bottom number minus the bottom number. For example, subtracting \(\begin{pmatrix}2\\3\end{pmatrix}\) from \(\begin{pmatrix}5\\7\end{pmatrix}\) gives \(5-2=3\) for the horizontal component and \(7-3=4\) for the vertical component, resulting in \(\begin{pmatrix}3\\4\end{pmatrix}\). Understanding this process is essential for physics problems, navigation, and further vector algebra, such as calculating distances or combining multiple movements. Practicing with multiple examples, including negative components, helps students internalize the component-wise approach and build confidence in applying vectors to real-world scenarios.