A position vector is the vector of an arrow drawn to from an origin to a point.

Look at the example below - a Cartesian plane in which we see points A A and B B

The position vector of A A connects the origin, marked O O , to A A - it can be written as a⃗ \vec a or OA→ \vec{OA} .

Similarly, the position vector of \(B\) connects the origin to B B - it can be written as b⃗ \vec b or OB→ \vec{OB}

It is important that the letters are written in this order. The vector BO→ \vec{BO} would connect B to the origin and therefore represents −b⃗ -\vec b .

If you are using Cartesian components to describe a position vector, the Cartesian coordinates of a point can be used to describe the position vector of that point.

For example, A A has the coordinates (1,4) (1,4) . This means its position vector can be written as a⃗ = \vec a=1ı⃗ +4ȷ⃗ 1 \vec{\imath} + 4 \vec{\jmath} or a⃗ =[14] \vec a= \begin{bmatrix}1\\4 \\\end{bmatrix} .

Similarly, B B has the coordinates (−3,−1) (-3,-1) . This means its position vector can be written as b⃗ = \vec b=−3ı⃗ +−1ȷ⃗ -3 \vec{\imath} + -1 \vec{\jmath} or b⃗ =[−3−1] \vec b= \begin{bmatrix}-3\\-1 \\\end{bmatrix} .

	Created by Niamh Ryan about 7 years ago

Part of our series on Vectors, learn more about position vectors in this study note with graphs and examples.

Position vectors