Position (geometry)

In <a href="/facts/Geometry/wTQf5ffQ">geometry</a>, a position or position vector, also known as location vector or radius vector, is a <a href="/facts/Euclidean_vector/bCLrdksy">Euclidean vector</a> that represents a <a href="/facts/Point_(geometry)/6YPAvX2a">point</a> P in <a href="/facts/Space/tq6LUM3C">space</a>. Its length represents the distance in relation to an arbitrary reference <a href="/facts/Origin_(mathematics)/Lm26tRCB">origin</a> O, and its <a href="/facts/Direction_(geometry)/Tj24mTJ8">direction</a> represents the angular orientation with respect to given reference axes. Usually denoted x, r, or s, it corresponds to the straight line segment from O to P.
In other words, it is the <a href="/facts/Displacement_(vector)/jkmEfS3C">displacement</a> or <a href="/facts/Translation_(geometry)/KlpWmnfX">translation</a> that maps the origin to P:

r
        
        =
        
          
            
              O
              P
            
            →
          
        
        .
      
    
    {\displaystyle \mathbf {r} ={\overrightarrow {OP}}.}

The term position vector is used mostly in the fields of <a href="/facts/Differential_geometry/c04XmyLu">differential geometry</a>, <a href="/facts/Mechanics/A3yHLQA5">mechanics</a> and occasionally <a href="/facts/Vector_calculus/mXKIJLJE">vector calculus</a>.
Frequently this is used in <a href="/facts/Two-dimensional/f4b397W8">two-dimensional</a> or <a href="/facts/Three-dimensional_space/KAqKWUbS">three-dimensional space</a>, but can be easily generalized to <a href="/facts/Euclidean_space/R2UbzmzM">Euclidean spaces</a> and <a href="/facts/Affine_space/tlvI3oX1">affine spaces</a> of any <a href="/facts/Dimension/0ktmUyac">dimension</a>.

Position (geometry) open-in-new

Position (geometry)