A Minimal Article Robert A. Beezer University of Puget Sound March 30, 2018 Abstract This is a very short article, but it still exercises some advanced features of MathBook XML.

This is a short paragraph to introduce the article (but it is not the abstract). It is optional, in case it would be preferable to have the first section be titled an “Introduction.”

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Some vector algebra essentials 1. Let a > 0 be a scalar, and v=(α, β, γ) = αi + βj + γk = αe1 + βe2 + γe3 be a vector in R3 with x-, y-, & z-components α, β, and γ. This vector has been written in the three most common ways used in current texts. The sets {i, j, k} and {e1 , e2 , e3 } represent the same set of unit vectors in mutually orthogonal directions in R3 . Be warned! We shall use all three forms interchangeably! (Ed. emphasis, not red) We then have >  

p |av| = a α2 + β 2 + γ 2 = 1 1 ⇐⇒ a = p α2 + β 2 + γ 2 =⇒ a unit vector in the direction of v is: v n= . |v|

2. Let u & v, be two non-parallel vectors:. . .

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Just Some Text

Now a single paragraph inside a titled section of the article.

 v    

  

>  

 

  av ⇐⇒ a > 1