Coordinate geometry

Vectors

What a vector is and how it differs from a scalar. Directed line segments, direction, parallel vectors, the coordinates of a vector and how to work out its magnitude.

Equations of a line

Parametric equations of a line in the plane and in space. The direction vector, deriving the equations from two points, restricting the parameter, and examples.

Relative position of two lines

The relative position of two lines in the plane: parallel, intersecting, perpendicular or coincident. How to tell from the equations and from the direction and normal vectors.

Equation of a plane

How to describe a plane using algebra. The parametric equations of a plane from a point and two vectors, how they follow from the equation of a line, and an example.

Distances

How to work out the distance from a point to a line. Using a ready-made formula, or the longer method through the coordinates of the foot of the perpendicular, with an example.

The circle

How to write a circle as an equation. Centre-radius form and general form, a circle given by its diameter, converting by completing the square, and the position of a point relative to a circle.