GCSE Maths Practice: vectors

Adding vectors involves combining corresponding components. For column vectors, the top number represents horizontal movement and the bottom represents vertical movement. Add the top numbers together and the bottom numbers together to get the resultant vector. For example, adding \(\begin{pmatrix}2\\3\end{pmatrix}\) and \(\begin{pmatrix}-1\\4\end{pmatrix}\) gives \(2+(-1)=1\) and \(3+4=7\), resulting in \(\begin{pmatrix}1\\7\end{pmatrix}\). This method ensures you account for direction and magnitude in each axis. Vector addition is used in physics, engineering, navigation, and computer graphics. Practicing with positive and negative components improves understanding of vector direction, magnitude, and how movements combine. Students should visualize vectors on a grid to reinforce the component-wise addition method and gain intuition about resultant vectors and displacement.