Position Vectors

This lesson covers position vectors, displacement vectors, and related concepts such as midpoints and dividing a line in a given ratio — as required by the Edexcel A-Level Mathematics specification (9MA0).

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What Is a Position Vector?

The position vector of a point P is the vector from the origin O to the point P. It is written as:

OP or simply p

If P has coordinates (3, 5, -2), then the position vector of P is:

p = (3, 5, -2) = 3i + 5j - 2k

Key Point: The position vector of a point tells you where the point is relative to the origin. Every point in space has a unique position vector.

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Displacement Vectors

The displacement vector from point A to point B is the vector that takes you from A to B. It is found by:

AB = b - a

where a and b are the position vectors of A and B respectively.

Example: A has position vector (2, 1, 3) and B has position vector (5, 4, -1). Find AB.