UNIT VECTOR-FREE VECTOR-POSITION VECTOR-NULL VECTOR

UNIT VECTOR-FREE VECTOR-POSITION VECTOR-NULL VECTOR

UNIT VECTOR

“A unit vector is defined as a vector in any specified direction whose magnitude
is unity i.e. 1. A unit vector only specifies the direction of a given vector. “

A unit vector is denoted by any small letter with a symbol of arrow hat ().

A unit vector can be determined by dividing the vector by its magnitude.

For example unit vector of a vector A is given by:

In three dimensional coordinate system unit vectors having the direction of the positive X-axis, Y-axi and Z-axis are used as unit vectors.These unit vectors are mutually perpendicular to each other.

FREE VECTOR

A vector that can be displaced parallel to itself and applied at any point is known as a FREE VECTOR.

A free vector can be specified by giving its magnitude and any two of the angles between the vector and coordinate axes.

POSITION VECTOR

Avector that indicates the position of a point in a coordinate system is referred to as POSITION VECTOR.

Suppose we have a fixed reference point O, then we can specify the position the position of a given point P with respect to point O by means of a vector having magnitude and direction represented by a directed line segment OP.This vector is called POSITION VECTOR.

In a three dimensional coordinate system if O is at origin then,O(0,0,0) and P is any point say P(x,y,z)

in this situation position vector of point P will be:

NULL VECTOR

A null vector is a vector having magnitude equal to zero.It is represented by . A null vector has no direction or it may have any direction. Generally a null vector is either equal to resultant of two equal vectors acting in opposite directions or multiple vectors in different directions.