Vectors (GCSE)

2D vectors as column matrices; addition, scalar multiplication, magnitude, parallelism. Higher-tier proofs.

A vector has magnitude and direction; a column vector (a; b) means a right, b up. Addition: component-wise. Scalar: multiply each component. Higher tier: vector-based geometric proofs (mid-points, parallel lines).

Worked examples

a + b: add components. a = (3; 1), b = (1; 4) ⇒ a + b = (4; 5).

2a = (6; 2). Parallel to a means same direction (or opposite if scalar negative).

Magnitude of (3; 4) = √(9+16) = 5.

Frequently asked questions

Bold or arrow?

GCSE writes vectors as bold lowercase (a, b) or with an arrow above. Both equivalent.

Position vectors?

From origin to a point. The position vector of A is OA. AB = OB − OA.