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This question already has an answer here:

also, who created these ? how to rotate 3-D vectors using quaternions ?

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marked as duplicate by Conifold, Alexandre Eremenko, Francois Ziegler, José Carlos Santos, tox123 May 30 '18 at 22:35

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  • $\begingroup$ You can see the post : what-were-the-criticisms-against-the-introduction-of-vector-analysis ? for details and references. $\endgroup$ – Mauro ALLEGRANZA May 17 '18 at 14:09
  • $\begingroup$ See also the Wiki's entry for the book A History of Vector Analysis. $\endgroup$ – Mauro ALLEGRANZA May 17 '18 at 14:10
  • $\begingroup$ And see Quaternion : History. $\endgroup$ – Mauro ALLEGRANZA May 17 '18 at 14:11
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    $\begingroup$ Thus, quaternions was discovered before the modern "codification" of vectors calculus. $\endgroup$ – Mauro ALLEGRANZA May 17 '18 at 14:13
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    $\begingroup$ Please google before asking here, Wikipedia has extensive history sections, e.g. for cross-product:"Oliver Heaviside in England and Josiah Willard Gibbs, a professor at Yale University in Connecticut, also felt that quaternion methods were too cumbersome, often requiring the scalar or vector part of a result to be extracted. Thus, about forty years after the quaternion product, the dot product and cross product were introduced". How to rotate vectors is a Math SE question. $\endgroup$ – Conifold May 17 '18 at 20:30