Editing Euclidean vector (section)

===Force, energy, work===
[[Force]] is a vector with dimensions of mass×length/time<sup>2</sup> (N m s <sup>−2</sup>) and [[Newton's second law]] is the scalar multiplication
<math display=block>{\mathbf F} = m{\mathbf a}</math>

Work is the dot product of [[force]] and [[displacement (vector)|displacement]]
<math display=block>W = {\mathbf F} \cdot ({\mathbf x}_2 - {\mathbf x}_1).</math>
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In physics, scalars may also have a unit of measurement associated with them. For instance, [[Newton's second law]] is
:<math>{\mathbf F} = m{\mathbf a}</math>
where '''F''' has units of force, '''a''' has units of acceleration, and the scalar ''m'' has units of mass. In one possible physical interpretation of the above diagram, the scale of acceleration is, for instance, 2 m/s<sup>2</sup> : cm, and that of force 5 N : cm. Thus a scale ratio of 2.5 kg : 1 is used for mass. Similarly, if displacement has a scale of 1:1000 and velocity of 0.2 cm : 1 m/s, or equivalently, 2 ms : 1, a scale ratio of 0.5 : s is used for time.
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