
Vectors 
Vectors describe a direction and magnitude in a coordinate system. For calculations we use them as lists of numbers. But for understanding it can help to display them as geometric objects. 
The vectorhas a magniutude 

Plot Vectors 
To draw a vector, use a coordinate system. Draw a horizontal line and a line perpendicular. The horizontal line is the Xaxis; the vertical line is the Yaxis. The axes labeled with numbers for the scales of the corresponding units. 
The following figure shows the vector or 
 The upper number is the xcoordinate and the lower the ycoordinate of the vector

To draw the vector (2, 3), move from its starting point 2 units on the xaxis to the right and 3 units on the yaxis to the top 

The vector is uniquely defined by its direction and its length. 

Equal Vectors 
The following figure shows parallel vectors of equal length, direction and orientation. Since the location of a vector is arbitrary, these vectors are equal. 


Opposite Vectors 
Parallel vectors of equal length but opposite in orientation are called opposite vector 

Parallel Vectors 
Two vectors are called in parallel if they have the same direction. They can be different lengths and have opposite orientations. 


