Position Vector

1. Position Vector
1. A vector , originating from point , is called the position vector of point relative to .
2. If and are the position vectors of points and , respectively, then the vector




2. Position Vectors of the Internal and External Division Points of a Line Segment
   If and are the position vectors of points and , respectively, and point divides the line segment internally in the ratio (with ), the position vector of is:
   
   
   If point divides the line segment externally in the ratio , the position vector of is:
   
   
   
   
3. Position Vector of the Centroid of a Triangle
   If , , and are the position vectors of points , , and , respectively, the position vector of the centroid of triangle is:
   
   
   If is the midpoint of line segment and is the position vector of , then:
   Since divides line segment in the ratio , the position vector of is given by: