Length of a vector

Length of a vector :
If v = ai+bj, then the length of v is
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

Example:
find the length of this vector. Let
Solution:

. to denote the vector We also use the notation

Exercise:

find the length of this vector. (1) Let
find the magnitude of this vector. (2) Let
find the norm of this vector. (3) Let

Scalar Multiplication:

Scalar multiplication can be accomplished component by component.
is a vector, then (1) If c is a scalar and
is a vector, then (2) If c is a scalar and

Since,






Example:
, then If c = -2 and




The Zero Vector:
The vector 0 = 0i+0j is called the zero vector , it is only vector whose length is Zero .