Introduction
It is useful to be able to describe vectors with reference to specific coordinate systems, such as the Cartesian coordinate system. So, in this Section, we show how this is possible by defining unit vectors in the directions of the $x$ and $y$ axes. Any other vector in the $xy$ plane can then be represented as a combination of these basis vectors . The idea is then extended to three dimensional vectors. This is useful because most engineering problems involve 3D situations.
Prerequisites
 be able to distinguish between a vector and a scalar
 be able torepresent a vector as a directed line segment
 understand the Cartesian coordinate system
Learning Outcomes

explain the meaning of the unit vectors
$\underset{\u0332}{i}$ , $\underset{\u0332}{j}$ and $\underset{\u0332}{k}$

express two dimensional and three
dimensional vectors in Cartesian form
 find the modulus of a vector expressed in Cartesian form
 find a ‘position vector’
Contents
1 Twodimensional coordinate frames1.1 Column vector notation
2 Threedimensional coordinate frames