Editing Euclidean vector (section)

===Position, velocity and acceleration===
The position of a point '''x''' = (''x''<sub>1</sub>, ''x''<sub>2</sub>, ''x''<sub>3</sub>) in three-dimensional space can be represented as a [[position vector]] whose base point is the origin
<math display=block>{\mathbf x} = x_1 {\mathbf e}_1 + x_2{\mathbf e}_2 + x_3{\mathbf e}_3.</math>
The position vector has dimensions of [[length]].

Given two points '''x''' = (''x''<sub>1</sub>, ''x''<sub>2</sub>, ''x''<sub>3</sub>), '''y''' = (''y''<sub>1</sub>, ''y''<sub>2</sub>, ''y''<sub>3</sub>) their [[Displacement (vector)|displacement]] is a vector
<math display=block>{\mathbf y}-{\mathbf x}=(y_1-x_1){\mathbf e}_1 + (y_2-x_2){\mathbf e}_2 + (y_3-x_3){\mathbf e}_3.</math>
which specifies the position of ''y'' relative to ''x''. The length of this vector gives the straight-line distance from ''x'' to ''y''. Displacement has the dimensions of length.

The [[velocity]] '''v''' of a point or particle is a vector, its length gives the [[speed]]. For constant velocity the position at time ''t'' will be
<math display=block>{\mathbf x}_t= t {\mathbf v} + {\mathbf x}_0,</math>
where '''x'''<sub>0</sub> is the position at time ''t'' = 0. Velocity is the [[#Ordinary derivative|time derivative]] of position. Its dimensions are length/time.

[[Acceleration]] '''a''' of a point is vector which is the [[#Ordinary derivative|time derivative]] of velocity. Its dimensions are length/time<sup>2</sup>.