Vectors

Vectors describe movement with both magnitude (size) and direction. For Edexcel GCSE Mathematics, all students need to understand column vectors for translations, and Higher tier students must also perform vector geometry proofs — showing that points are collinear, finding midpoints, and determining ratios.

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Key Vocabulary

Term	Meaning
Scalar	A quantity with magnitude only (e.g. speed, mass)
Vector	A quantity with both magnitude and direction (e.g. velocity, displacement)
Column vector	A vector written as (x over y) showing horizontal and vertical components
Magnitude	The length (size) of a vector
Parallel vectors	Vectors that are scalar multiples of each other (same or opposite direction)
Collinear	Points that lie on the same straight line
Position vector	The vector from the origin to a point
Resultant	The single vector that has the same effect as two or more vectors combined

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Column Vectors