GCSE Maths Practice: vectors

Vectors in two dimensions can be manipulated using certain operations. The primary valid operations are: addition, subtraction, and multiplication by a scalar. Adding two vectors involves summing their corresponding components to get a resultant vector. Subtracting vectors is done similarly but component-wise in the reverse order. Multiplying a vector by a scalar changes its magnitude and possibly its direction, depending on the scalar's sign. However, vectors cannot be multiplied directly by each other like numbers; dot or cross products are advanced concepts and not standard GCSE operations. Understanding which operations are valid ensures accurate calculations in geometry, physics, and engineering problems involving forces or displacements. Practicing with a variety of vector operations helps students internalize rules and develop intuition for component-wise calculations and resultant vectors.