GCSE Maths Practice: vectors

Column vectors represent movements in two dimensions. The top component represents horizontal movement, and the bottom component represents vertical movement. A leftward movement is represented by a negative top component, while no vertical movement is represented by a zero bottom component. For example, moving 5 units left and 0 units vertically is written as \(\begin{pmatrix}-5\\0\end{pmatrix}\). Understanding how to correctly assign positive and negative signs to vector components is critical for solving coordinate geometry problems, physics displacement problems, and plotting movements on a grid. Practicing with left, right, up, and down movements helps students visualize vectors and prevents errors in calculation. This knowledge is also applied when combining vectors using addition, subtraction, or scalar multiplication, ensuring accuracy in resultant vectors and directions.