- A-Level Maths

# Vectors

A vector is a quantity with both **magnitude and direction, **and is typically represented visually by a line segment between two points.

There are many ways of representing vectors in notation:

The two points that the vector connects with an

**arrow above them**As a

**bold typeface**lower case letterAs an

__underlined lower case letter__As a

**column vector**, showing displacement in the x-direction above that in the y-directionAs a multiple of

**unit vectors**,**i**(one unit in the positive x-direction) and**j**(one unit in the positive y-direction)

These notes will predominantly use **bold typeface** of lower case letters, __underlined__ letters and the unit vectors **i** and **j**.

Vectors can be **multiplied by a scalar, and added and subtracted:**

## Magnitude & Direction

The **magnitude **of a vector is given by Pythagoras' Theorem. Magnitude is noted using straight lines on either side of the letter, like modulus.

For the vector=axi+yj,|= √(a|x²+y²)

A** unit direction vector, â**, can be found as **a** / **|a|**

A vector can also be defined by giving its magnitude and the angle it makes with one of the coordinate axis. This is called **magnitude-direction form**.