Definitions/Operations
Definition
Expressing magnitude and direction
The length and direction of the segment from point
to point 
can be expressed as 
.The magnitude of
is expressed as 
and is denominated as a scalar.If
, then 
is denominated as a unit vector.Equal sign
The magnitude and direction of
are equal
are not in the same line and 
is a parallelogram.
Addition
A vector that starts at the starting point of
and ends at the ending point of 
Commutative law
Associative law
Subtraction
A vector that starts at the ending point of
and ends at the ending point of 
, when 
and 
share the same starting point.
Multiplication by a real number
If
:
has the same direction as 
and magnitude 
.
:
has the opposite direction of
and magnitude 
.If
:
Associative law
Distributive law
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