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:::At the level of this article vector algebra is done in 3D. E.g. you have the cross product, defined only in three dimensions, as a key operation. This and the dot product show how it is a 'vector' part as both operations arise directly from the quaternion product if restricted to products only of the vector parts. At least that's how I learned it. I later learned how to generalise it in various ways, which leads to other ways to think of the non-scalar parts, as imaginaries, as bivectors . But vectors I think is most usual at a less advanced level.--<small>[[User:JohnBlackburne|JohnBlackburne]]</small><sup>[[User_talk:JohnBlackburne|words]]</sup><sub style="margin-left:-2.0ex;">[[Special:Contributions/JohnBlackburne|deeds]]</sub> 00:21, 12 March 2015 (UTC)
::: Just because quaternions can be related to vectors and rotations in Euclidean 3-space doesn't mean that it is their nature or purpose, it's just a use you can make of them. So I disagree with the argument that the imaginary part of a quaternion is a vector in a "very real sense". And the "scalar part" term is no more clever imho, why would you want to think of it as a scalar? It is just a quaternion that is identified as a real. I recall that scalars are what you name the elements of the base field of a vector space, when you think of them acting on vectors by multiplication. If you work with vector spaces over the quaternions, then the quaternions themselves are all scalars. I also recall that in (
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