8. Motion in three dimensions

8. Motion in three dimensions

• We have already studied physical quantities like displacement ,velocity,acceleration etc in one and two dimension
• In this topic ,we will generalize our previous knowlegde 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_xi+v_yj+v_zk where v_x=dx/dt,v_y=dy/dt and v_z=dz/dt
  and
  a=v_xi+a_yj+a_zk
  where a_x=dv_x/dt,a_y=dv_y/dt and a_z=dv_z/dt
• All the relations we have derived incase of motion in plane are valid for 3-D motion with one added co-ordinate