## Physics XI Content

# UNIT VECTOR-FREE VECTOR-POSITION VECTOR-NULL VECTOR

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UNIT VECTOR | |||

“A unit vector is defined as a vector in any specified direction whose magnitudeis 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 | |||

A vector 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 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. | |||