Vectors

Introduction

Vectors

• A vector describes a movement from one point to another. A vector quantity has both direction and magnitude (size).
• A scalar quantity has only magnitude.
• A vector can be represented by a line segment labelled with an arrow.
  
• A vector between two points A and B is described as:  a or a 
  
• The vector can also be represented by the column vector
  The top number tells you how many spaces or units to move in the positive x-direction and the bottom number is how many to move in the positive y-direction.
  Vectors are equal if they have the same magnitude and direction regardless of where they are.
  
  
• A negative vector has the same magnitude but the opposite direction.
  
• Vector - k is the same as travelling backwards down the vector k.

Example: Write, in terms of a, b and c, the vectors  and

  are equal vectors, they have the same magnitude and direction.

 are equal vectors, they have the same magnitude and direction.

 has the same magnitude as  but the opposite direction.

 has the same magnitude as  but the opposite direction.