# 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 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**=x**i**+y**j**+z**k**

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

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