GCSE Maths Practice: vectors
This question teaches how to write column vectors for translations in the plane.
Top positive → right, bottom positive → up. Check with a simple sketch.
Column vectors express movement in two dimensions: horizontal (x-axis) and vertical (y-axis). To write a vector for 4 units right and 3 units up, assign the top component as +4 (right) and the bottom component as +3 (up), giving \(\begin{pmatrix}4\\3\end{pmatrix}\). Positive components indicate right or upward movement, while negative components indicate left or downward movement. Being able to translate verbal descriptions of movement into vectors is essential in coordinate geometry, physics, and navigation. Visualization helps: plotting the initial point and adding the vector shows the final position. Practicing with different directions, magnitudes, and combinations of movements strengthens understanding of vector notation, addition, and scalar multiplication. Recognizing patterns in vector components aids in solving problems like displacement, motion, and resultant vectors efficiently.