Absolute Position, Relative Position, Displacement and Distance Travelled of an Object

1. Position of any Object is a Place/Location where the Object Exists. It is a Vector Quantity.
2. The Absolute Position of Any Object in a Coordinate System / Reference Frame is the Location/Position of that Object with respect to the Origin of that Coordinate System / Reference Frame. Given any 2 Objects \(A\) and \(B\), their Absolute Position is given by their Position Vectors \(\vec{R_A}\) and \(\vec{R_B}\) respectively.
3. The Relative Position of Any Object \(A\) with respect to Any Other Object \(B\) (\(\vec{R_{AB}}\)) is given by the Difference of their Absolute Position Vectors as follows
   
   \(\vec{R_{AB}}=\vec{R_A}-\vec{R_B}\)   ...(1)
   
   Similarly, the Relative Position of the Object \(B\) with respect to Object \(A\) (\(\vec{R_{BA}}\)) is given by the Difference of their Absolute Position Vectors as follows
   
   \(\vec{R_{BA}}=\vec{R_B}-\vec{R_A}\)   ...(2)
   
   Please note that \(\vec{R_{AB}}=-\vec{R_{BA}}\)    ...(3).
4. If Any 2 Sets of Relative Position between 3 Objects are known, then the Third Set can be found out by Triangle Law of Vector Addition/Subtraction. For example, given any 3 Objects \(A\), \(B\) and \(C\) having Absolute Positions \(\vec{R_A}\), \(\vec{R_B}\) and \(\vec{R_C}\) respectively, then
   
   \(\vec{R_{AC}}=\vec{R_{AB}} + \vec{R_{BC}}\)   ...(4)   (as per Triangle Law of Vector Addition/Subtraction)
   
   Using the above formula, if any 2 of \(\vec{R_{AB}}\) (or \(\vec{R_{BA}}\)) , \(\vec{R_{BC}}\) (or \(\vec{R_{CB}}\)) and \(\vec{R_{AC}}\) (or \(\vec{R_{CA}}\)) are known, the third can be found out.
5. For Any Object that changes its Position, Displacement is the Difference between its Final Position and Initial Position. It is a Vector Quantity and is also called the Displacement Vector. For e.g given any Object \(A\) having Initial Position as \(\vec{R_{A_{I}}}\) and Final Position as \(\vec{R_{A_{F}}}\), the Displacement Vector \(\vec{R_{A_{D}}}\) is calculated as
   
   \(\vec{R_{A_{D}}}=\vec{R_{A_{F}}} - \vec{R_{A_{I}}}\)   ...(5)
6. Distance Travelled by an Object for a Displacement is given by the Magnitude of the Displacement Vector. It is a Scalar Quantity. For e.g Distance Travelled by an Object \(A\) (\(D_{A}\)) having a Displacement Vector \(\vec{R_{A_{D}}}\) is calculated as
   
   \(D_{A}=|\vec{R_{A_{D}}}|\)   ...(6)