Vector Calculation 
In the following descriptin are vector operations using vectors of length two or three. Vectors can have any number of entries. 

Vector Addition 
Vectors can only be added if the number of dimensions and their orientation (columns or roworiented) are the same. 
The vectors and can be added

The vectors and can not be added


Each number in the list is called a element. Vectors can be
added and subtracted by adding and subtracting the elements. 


Example: 

The addition to higherdimension vectors is performed according to the same principle. 

Graphic Vector Addition 
The following figure shows the graphical vector addition of the expression 


Vector Subtraction 
The subtraction of vectors is identical to the addition of vectors, but with negative operator. For the vector subtraction, the same rules apply as for the addition of vectors. 
Vector Multiplication 
Vectors also can be multiplied by real numbers, as follows. 

The answer is a real number, not a vector. 

Scalar multiplication of a vector 
Scalar vector multiplication is the multiplication of a vector with a real number. For this purpose, each element of the vector is multiplied by the real number. 
Example: 



