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

  $\underset{̲}{i}$ , $\underset{̲}{j}$ and $\underset{̲}{k}$

• express two dimensional and three

  dimensional vectors in Cartesian form

• find the modulus of a vector expressed in Cartesian form
• find a ‘position vector’

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