LaTeX is a typesetting language used for creating technical and scientific documents, particularly in the fields of mathematics, computer science, and engineering.
To format a vector expression in LaTeX, use the \vec{} command followed by the vector's components in curly brackets. For example, \vec{a} = (a_1, a_2, a_3) would produce a vector a with components a1, a2, and a3.
A vector is a quantity that has both magnitude and direction, while a scalar is a quantity that only has magnitude. In other words, a vector is represented by both a size and a direction, while a scalar is only represented by a size.
Some common mistakes to avoid when writing vector expressions in LaTeX include forgetting to use the \vec{} command, using the wrong symbols for vector operations (e.g. using * for dot product instead of \cdot), and not properly enclosing the vector's components in curly brackets.
There are many online resources available for learning more about using LaTeX for technical and scientific documents. Some popular websites include Overleaf, ShareLaTeX, and LaTeX-Tutorial.com. You can also find various books and tutorials on the subject.