We have already studied physical quantities like displacement ,velocity,acceleration etc in one and two dimension

In this topic ,we will generalize our previous knowledge of motion in 1 and 2 -dimension to three dimension's

As we have used vectors to represent motion in a plane,we can freely use vectors and its properties in 3-dimension as we have done in case of motion in a plane

In three dimensions ,we have three units vectors i ,j and k associated with each co-ordinate axis of Cartesian co-ordinates system shown below in the figure

Consider a particle moving in 3-D space .Let P be its position at any point t.Position vector of this particle at point P would be r=xi+yj+zk
Where x,y and z are co-ordinates of point P

Similarly velocity and acceleration vectors of particle moving in 3-D space are v=v_{x}i+v_{y}j+v_{z}k
where v_{x}=dx/dt,v_{y}=dy/dt and v_{z}=dz/dt
and a=v_{x}i+a_{y}j+a_{z}k
where a_{x}=dv_{x}/dt,a_{y}=dv_{y}/dt and a_{z}=dv_{z}/dt

All the relations we have derived in case of motion in plane are valid for 3-D motion with one added co-ordinate