GCSE Maths Practice: vectors

Question 9 of 10

This question teaches how to interpret the components of a column vector.

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\( \begin{array}{l}\text{Which statements about column vectors are correct?}\end{array} \)

Select all correct options:

Top number → horizontal (x), bottom number → vertical (y). Sketch to visualize.

Column vectors are used to represent movement or displacement in two-dimensional space. The top number indicates movement along the horizontal axis (x-direction) and the bottom number indicates movement along the vertical axis (y-direction). Understanding how to read vectors is essential before performing vector operations like addition, subtraction, and scalar multiplication. For instance, a vector \(\begin{pmatrix}3\\-2\end{pmatrix}\) moves 3 units to the right and 2 units down. When analyzing problems in coordinate geometry, physics, or navigation, knowing which component affects which axis ensures accurate plotting and correct vector calculations. Misinterpreting the components can lead to incorrect results in vector sums, differences, or translations. Practicing identifying and describing the direction and magnitude of vectors strengthens comprehension and prepares students for more advanced applications like resultant vectors, vector decomposition, and motion analysis. Always visualize the movement on a grid to reinforce understanding.