Written and maintained by CASRAI Editorial Board
Last updated
In LaTeX there is no single “vector product” command: the cross product is conventionally typed with \times between two vector symbols, the dot (scalar) product with \cdot, and vectors themselves are marked with \mathbf{...} or \vec{...}. This guide gives the exact code for each, separates the vector products from look-alike symbols (\prod, \otimes, \wedge), and shows copy-paste examples you can compile in Overleaf. Written for researchers typesetting physics, engineering or statistics notation.
Note on what is sourced: which symbol means “cross” or “dot” is mathematical notation convention, not something the LaTeX documentation defines. The documentation sources cited below confirm that the commands exist and what category they belong to.
What it is used for in research
Vector products appear in mechanics, electromagnetism, fluid dynamics, computer graphics and multivariate statistics. In a manuscript you usually need three things: the operator symbol, a way to show that the operands are vectors, and correct math-mode delimiters. The word “product” is also overloaded: a big capital-pi product over an index is a different object from a vector product, which is why searches for this topic return both.
Which command for which product
The commands below are all documented in the Overleaf symbol list or the LaTeX Wikibooks mathematics chapter. The meaning in the second column is the usual mathematical convention.
| Product | Usual notation | LaTeX code | Documented as |
|---|---|---|---|
| Cross (vector) product | a × b | \mathbf{a} \times \mathbf{b} |
\times is a binary operator (Overleaf, Wikibooks) |
| Dot (scalar) product | a · b | \mathbf{a} \cdot \mathbf{b} |
\cdot is the binary multiplication operator (Wikibooks) |
| Wedge (exterior) product | a ∧ b | a \wedge b |
\wedge is in the binary operation list (Overleaf, Wikibooks) |
| Tensor / outer-product style symbol | a ⊗ b | a \otimes b |
\otimes is in the binary operators table (Overleaf) |
| Cartesian product of sets | A × B | A \times B |
same \times operator, used between sets |
| Product over an index (not a vector product) | ∏ xi | \prod_{i=1}^{n} x_i |
\prod is a big operator (Wikibooks) |
The same \times serves the cross product and the Cartesian product; the operands tell the reader which is meant. See the related guides on blackboard-bold sets with mathbb and set operators in LaTeX when the operands are sets.
Install or access (official source only)
- Online: the Overleaf editor needs no installation. See what Overleaf is and collaborative LaTeX alternatives.
- Local install: the AMS packages are distributed on CTAN. The CTAN page for
amsmath(ctan.org/pkg/amsmath, read 2026-11-07) lists it as the main package of AMS-LaTeX, maintained by the LaTeX Project Team under the LPPL 1.3c, withamsldoc.pdfas the user guide. Loadingamsmathalso loadsamsbsy, which provides bold symbols. Add\usepackage{amsmath}to the preamble.
Step-by-step: typeset vector products
- Open a document with a math environment. Overleaf’s mathematical-expressions page documents inline delimiters
\( ... \),$ ... $and\begin{math}...\end{math}(it states the choice among them is a matter of taste) and display delimiters\[ ... \],\begin{displaymath}and\begin{equation}. - Mark the vectors. Use
\mathbf{a}for bold vectors (the Wikibooks font table lists\mathbfas the bold font, commonly used for vectors) or\vec{a}for an arrow over the letter. For a long arrow over several letters use\overrightarrow{AB}. - Add the operator. Type
\timesfor the cross product or\cdotfor the dot product between the two vector symbols. - Set the result. Write the relation as ordinary math:
\mathbf{c} = \mathbf{a} \times \mathbf{b}. - Compile and check the output against the table above.
Copy-paste examples
Inline cross product, bold style:
The torque is \( \boldsymbol{\tau} = \mathbf{r} \times \mathbf{F} \).Display dot product, arrow style:
\[ \vec{a} \cdot \vec{b} = a_1 b_1 + a_2 b_2 + a_3 b_3 \]Numbered equation:
\begin{equation}
\mathbf{c} = \mathbf{a} \times \mathbf{b}
\end{equation}Index product, for contrast:
\[ \prod_{i=1}^{n} x_i \]Choosing a vector marking style
| Style | Code | What the documentation says |
|---|---|---|
| Bold | \mathbf{a} |
Listed as the bold math font, commonly used for vectors (Wikibooks) |
| Bold Greek or other symbols | \boldsymbol{\tau} |
Recommended for bold lowercase Greek and other symbols; works only if a bold version of the symbol exists in the current font (Wikibooks) |
| Short arrow | \vec{a} |
Accent that places an arrow over the letter (Wikibooks) |
| Long arrow | \overrightarrow{AB} |
Long arrow over several characters (Wikibooks) |
Pick one style and use it throughout a document; mixing bold and arrow styles for the same kind of object confuses readers. For text-mode bold and the bm package, see the LaTeX boldface guide.
Output and how to read it
The cross-product example renders as a bold or arrowed pair of symbols joined by a multiplication cross; the dot-product example renders with a centred dot. In display mode the equation sits on its own line; in inline mode it flows with the sentence. Overleaf’s documentation notes that how an equation is displayed depends on the delimiter you choose, so use display delimiters for formulas you want to stand out or number.
Troubleshooting
- Greek letter is not bold with
\mathbf. Use\boldsymbol{...}instead (Wikibooks). It only works if the current font has a bold version of that symbol. - Symbols look wrong or error. Make sure the command sits inside one of the math delimiters listed in step 1 rather than in plain text.
- The cross and dot look like ordinary multiplication. That is expected: LaTeX renders the symbol only. Whether it denotes a vector product depends on the vector styling around it and on the definition you give the reader.
- You need a custom name for an operator.
\DeclareMathOperatortakes two parameters (the command name and the displayed text) and requiresamsmath;\DeclareMathOperator*is for operators whose subscripts are set as limits (Overleaf Operators page). - Greek letters in vector names. See the Greek symbol guide for the commands.
Free alternatives and other places the code works
| Option | Use |
|---|---|
| Overleaf online editor | Compile the examples in the browser; the symbol and expression documentation cited here is Overleaf’s own. |
Local LaTeX with amsmath from CTAN |
Compile offline; amsmath is distributed on CTAN as described above. |
| MathJax on web pages | Render LaTeX-style math in a browser; see the MathJax LaTeX guide. |
FAQ
What is the LaTeX code for the cross product?
Use \times between two vector symbols, for example \mathbf{a} \times \mathbf{b}. \times is documented as a binary operator in the Overleaf symbol table; using it for the cross product is standard notation.
What is the LaTeX code for the dot product?
Use \cdot, for example \mathbf{a} \cdot \mathbf{b}. The Wikibooks mathematics chapter describes \cdot as the binary multiplication operator.
Is \prod the vector product?
No. \prod is a big operator for products over an index, such as \prod_{i=1}^{n} x_i. It is the other meaning of “product” that shares the search results with vector products.
How do I write the symbol for the wedge or tensor product?
Use \wedge for the wedge symbol and \otimes for the tensor-product symbol; both appear in the Overleaf operator tables.
Bold or arrow for vectors?
Either works. \mathbf and \vec are both documented; choose one and apply it consistently.
Sources
- Overleaf, List of Greek letters and math symbols: overleaf.com/learn/latex/List_of_Greek_letters_and_math_symbols (read 2026-11-07)
- Overleaf, Mathematical expressions: overleaf.com/learn/latex/Mathematical_expressions (read 2026-11-07)
- Overleaf, Operators: overleaf.com/learn/latex/Operators (read 2026-11-07)
- Wikibooks, LaTeX/Mathematics: en.wikibooks.org/wiki/LaTeX/Mathematics (read 2026-11-07)
- CTAN, amsmath package: ctan.org/pkg/amsmath (read 2026-11-07)
