Position vectors 2d

Introduction to Position Vectors in 2D

A vector is a quantity that has both magnitude (size) and direction.
A position vector, in particular, describes a specific position in space with reference to an origin.
In 2D, this is usually the point (0,0) on a cartesian grid.
Position vectors are often represented on diagrams as an arrow from the origin to the point in question.
In general, the position vector of a point P is denoted as OP (origin to point P).

Formal Representation

A position vector in 2D is represented as a column matrix, or ordered pair, such as (x, y).
x represents the displacement from the origin in the x-direction (horizontal).
y represents the displacement from the origin in the y-direction (vertical).
For example, a position vector (5,3) indicates a position 5 units to the right and 3 units up from the origin.

Vector Maths

It’s possible to add and subtract vectors, and also to multiply vectors by a scalar (a single number).
Adding vectors is equivalent to following the arrows one after the other. So OP + PQ = OQ.
Subtracting vectors gives the relative position: subtract OQ - OP to get the vector PQ.
When multiplying a vector by a scalar, both the x and y components of the vector are multiplied by this number.

Practical Applications

Understanding position vectors is key to physics, computer graphics, and many engineering disciplines.
They allow us to simplify and solve real-world problems involving directions and positions.

For revisions, try plotting position vectors on a 2D grid and manipulating them. Also, practice vector addition, subtraction and scalar multiplication for a variety of vectors.