Given two vectors in \(\mathbb{R}^{n}\), there are two main operations that are defined between them:
- First there is the sum of the two vectors, which gives another vector in \(\mathbb{R}^{n}\).
- Second, there is the dot product, which is an operation that gives a positive real number.
In the case in which \(n=3\), there is a third operation called the vector product
, which yields another vector with very special properties.
1. Dot product command in LaTeX
The dot product between two vectors \(u\) and \(v\) is usually denoted with a dot between them, \(u\cdot v\). This dot is produced in math mode with the command \cdot, and thus the previous expression was obtained with
$u\cdot v$
2. Dot product (angular brackets notation) in LaTeX
However, there are other schools that prefer to use a more cumbersome, but in my modest opinion, more readable and clear notation, surrounding both vectors with angular brackets: \(\left< u,v \right>\). This is produced with:
$\left< u, v \right>$
Although this is not the only way to obtain that same output, it is the most general, since the brackets will grow in size to fit the content. However, the same result (without growing brackets) can be obtained with:
$\langle u,v \rangle$
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