vector whose magnitude is unity i.e. equal to 1 is called unit vector.

It is represented as n^{^}  (read as n cap). Unit vectors along X-, Y-, Z-axes are i^{^}, j^{^} , k^{^} .

a unit vector is a vector having unit magnitude 1 ex-i^

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) whose length is 1 (the unit length). A unit vector is often denoted by a lowercase letter with a superscribed caret or “hat”,  (pronounced "i-hat").



In Euclidean space, the dot product of two unit vectors is simply the cosine of the angle between them. This follows from the formula for the dot product, since the lengths are both 1.



The normalized vector or  of a non-zero vector  is the unit vector codirectional with  , i.e.,



where  is the norm (or length) of . The term normalized vector is sometimes used as a synonym for unit vector.



The elements of a basis are usually chosen to be unit vectors. Every vector in the space may be written as a linear combination of unit vectors. The most commonly encountered bases are Cartesian, polar, and spherical coordinates. Each uses different unit vectors according to the symmetry of the coordinate system. Since these systems are encountered in so many different contexts, it is not uncommon to encounter different naming conventions than those used here.

 

unit vector iz a vestor wid magnitude 1.....

it just shows d direction...i^ j^ nd k^ r unit vectors along x axis ,y axis nd z axis...

a quantity of value 1 used to denote directions.

Unit vector



Unit vector has a magnitude of one and is directed in a particular direction. It does not have dimension or unit like most other physical quantities. Thus, multiplying a scalar by unit vector converts the scalar quantity into a vector without changing its magnitude, but assigning it a direction.

Conventionally, unit vectors along the rectangular axes is represented with bold type face symbols like :  i , j and k