TYPES OF VECTORS

VECTOR NOTATION

For example this arrow represents a vector. The direction is given by the arrow, while the length of the line represents the magnitude.

This vector can be written as:  , a, or  .

In print, a is written in bold type. In handwriting, the vector is indicated by putting a squiggle underneath the letter:  

QUESTION

Write down the 3 ways to describe the vector if the arrow is now pointing from B to A.

Answer

Remember that the arrow describes the direction. So, in this case, the vector is from B to A. If we move 'backwards' along a vector, it becomes negative, so a becomes -a. Moving from B to A entails moving 3 units to the left, and 4 down.

So the three ways to write this vector are:

 , -a and 

VECTOR REPRESENTION

EXAMPLE OF VECTOR REPRESENTION :

EQUALITY OF VACTOR

Two vectors are said to be equal if they have the same magnitude and direction. In the figure below, three equal vectors  have been represented. The equality of vectors is expressed in the following way 

Since the three vectors have the same direction,

Moreover, the three vectors are also equal in magnitude.

If the scales selected for the representation of three vectors are the same, then, three equal vectors are represented by three arrows of equal lengths, pointing in the same direction. If, however, the scales chosen are different, then, it is possible to represent equal vectors by arrows of different lengths. Equality of two vectors does not depend upon their location in space. A direct consequence of this physical fact is that a vector can be displaced parallel to itself. This fact may be used in testing the equality of two vectors. It would be of interest to note that, to compare two vectors with different physical dimensions, would be absolutely meaningless. For example, it is not possible to compare a velocity vector with a force vector.

NEGATIVE VACTOR

The negative sign reverses the direction of the vector.

      EXAMPLE

      

      EXAMPLE