GCSE Maths Practice: vectors

Adding vectors involves combining their corresponding components. For column vectors, the top component represents horizontal movement and the bottom represents vertical movement. To add two vectors, add the top numbers together to get the horizontal component of the resultant vector, and add the bottom numbers together to get the vertical component. For example, adding \(\begin{pmatrix}2\\3\end{pmatrix}\) and \(\begin{pmatrix}-1\\4\end{pmatrix}\) yields \(\begin{pmatrix}2+(-1)\\3+4\end{pmatrix} = \begin{pmatrix}1\\7\end{pmatrix}\). This component-wise addition preserves both magnitude and direction of the original vectors. Understanding vector addition is essential in physics for forces and motion, in engineering for displacement analysis, and in coordinate geometry for calculating translations and resultant vectors. Visualizing vector addition on a grid helps students internalize the concept and accurately predict the direction and length of the resulting vector. Practice with positive and negative components reinforces mastery and prepares students for more advanced operations like scalar multiplication and vector subtraction.