Editing Unit vector (section)

===General unit vectors===

{{main|Orthogonal coordinates}}

Common themes of unit vectors occur throughout [[physics]] and [[geometry]]:<ref>{{cite book|title=Calculus (Schaum's Outlines Series)|edition=5th|publisher=Mc Graw Hill|author1=F. Ayres |author2=E. Mendelson |year=2009|isbn=978-0-07-150861-2}}</ref>

{| class="wikitable"
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! scope="col" width="200" | Unit vector
! scope="col" width="150" | Nomenclature
! scope="col" width="410" | Diagram
|-
| Tangent vector to a curve/flux line || <math> \mathbf{\hat{t}}</math> || rowspan="3" | [[File:Tangent normal binormal unit vectors.svg|200px|"200px"]] [[File:Polar coord unit vectors and normal.svg|200px|"200px"]]
A normal vector <math> \mathbf{\hat{n}} </math> to the plane containing and defined by the radial position vector <math> r \mathbf{\hat{r}} </math> and angular tangential direction of rotation <math> \theta \boldsymbol{\hat{\theta}} </math> is necessary so that the vector equations of angular motion hold.
|-
|Normal to a surface tangent plane/plane containing radial position component and angular tangential component
|| <math> \mathbf{\hat{n}}</math>

In terms of [[spherical coordinate system|polar coordinates]];
<math> \mathbf{\hat{n}} = \mathbf{\hat{r}} \times \boldsymbol{\hat{\theta}} </math>
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| Binormal vector to tangent and normal
|| <math> \mathbf{\hat{b}} = \mathbf{\hat{t}} \times \mathbf{\hat{n}} </math><ref>{{cite book|title=Vector Analysis (Schaum's Outlines Series)|edition=2nd|publisher=Mc Graw Hill|author1=M. R. Spiegel |author2=S. Lipschutz |author3=D. Spellman |year=2009|isbn=978-0-07-161545-7}}</ref>
|-
| Parallel to some axis/line || <math> \mathbf{\hat{e}}_{\parallel} </math> || rowspan="2" | [[File:Perpendicular and parallel unit vectors.svg|200px|"200px"]]
One unit vector <math> \mathbf{\hat{e}}_{\parallel}</math> aligned parallel to a principal direction (red line), and a perpendicular unit vector <math> \mathbf{\hat{e}}_{\bot}</math> is in any radial direction relative to the principal line.
|-
| Perpendicular to some axis/line in some radial direction
|| <math> \mathbf{\hat{e}}_{\bot} </math>
|-
| Possible angular deviation relative to some axis/line
|| <math> \mathbf{\hat{e}}_{\angle} </math>
|| [[File:Angular unit vector.svg|200px|"200px"]]
Unit vector at acute deviation angle ''φ'' (including 0 or ''π''/2 rad) relative to a principal direction.
|-
|}