Unit vectors in the Direction of v

Unit vectors in the Direction of v:

A vector is called a unit vector if it has magnitude = 1 , if a vector v = ai+bj then the unit vector in the direction of v can be found by :

unit vector = u = v/(norm of v)


Example:
the unit vector in the direction of v = -3i+j is:




Since:


Example:
Let v = 3i-4j find the unit vector in the direction of v .
Solution :



Vectors in space:

Addition, Subtraction and Scalar Multiplication for vectors in space:
,and and For any vectors for any scalar c,






The Vector between Two points:

is: to The vector from

Example:
is: to The vector from


vector :
, then the length of v is If
represented by: Length of
, which is read (the The usual symbol for the length is
length of v or the magnitude of v, the latter being more common in applied fields. The bars are the same as the ones we use for absolute values.
Notation:
is called the The length of a vector
norm or magnitude of v.
The length of a vector v can be written as