Kinematics in Three Dimension

4.1 Position and Displacement
The purpose of this section is to generalize the previously introduced concept of displacement, velocity and acceleration in order to deal with motion in three dimension.
A position vector ??? can be written as:
???=?????+?????+????? (1)
where ?????,????? and ????? are the vector components of ???. A particle moves from A with position vector ????? to B the position vector ????? during a certain time interval, as shown in figure 1, then the particle’s displacement ???? is :
????=??????????? (2)
????=(???????+???????+???????)?(???????+???????+???????)
????=(?????????)???+(?????????)???+(?????????)??? (3)
Or
????=??????+??????+?????? (4)
Where
???=????????? , ???=????????? and ???=?????????
4.2 Velocity and Acceleration
Consider a particle in a plane moving from P to Q the change in position vector is ????:
????=??????+?????? (5)
Let ??? be the time interval foe the motion from P to Q
The average velocity of the particle is then defined as the vector quantity equal to the displacement divided by the time interval: ???????=???????=?????????+?????????+????????? (6)
Let ???
??=?????? , ???
??=?????? and ???
??=??????
???=???
??+???
??+??