Dot Operator

The Mathematical Symbol "Dot Operator (⋅)"

homesitemapsymbolsdot operator

The Dot Operator (⋅): An Insight

The Dot Operator, symbolized as ⋅ is a mathematical notation frequently employed in various mathematical contexts. One of its primary usages is in vector calculus, where it represents the dot product. Additionally, it can denote multiplication in some scenarios, especially when traditional multiplication signs might be confusing. In this article, we'll dive deep into the significant applications of this symbol with a pair of examples for each use.

1. Vector Calculus: Dot Product

In vector calculus, the ⋅ notation denotes the dot product (or scalar product) of two vectors. This operation yields a scalar value and is defined for two vectors as the product of their magnitudes and the cosine of the angle between them.

Example 1:

Given two vectors \(\mathbf{A}\) and \(\mathbf{B}\), their dot product is represented as:

\(\mathbf{A} ⋅ \mathbf{B} = |\mathbf{A}| |\mathbf{B}| \cos(\theta)\)

Where \( \theta \) is the angle between \(\mathbf{A}\) and \(\mathbf{B}\).

Example 2:

For vectors \(\mathbf{A} = [a_1, a_2]\) and \(\mathbf{B} = [b_1, b_2]\) in a 2-dimensional space:

\(\mathbf{A} ⋅ \mathbf{B} = a_1 \times b_1 + a_2 \times b_2\)

2. Multiplication Representation

Occasionally, the ⋅ symbol is used to represent multiplication, especially in contexts where the traditional multiplication signs (like \( \times \)) might cause confusion.

Example 1:

When dealing with algebraic variables:

\(a ⋅ b\), which simply means \(a \times b\).

Example 2:

In scalar multiplication:

\(5 ⋅ 3 = 15\)

These instances showcase the versatility of the Dot Operator in various mathematical scenarios. As with many mathematical symbols, context is crucial for interpreting its precise meaning.

Mathematical symbol 'Dot Operator'

Are You Good at Mathematical Symbols?

Do you know, or can you guess, the technical symbols? Well, let's see!
gold cup

gold cup

gold cup

  • This test has questions.
  • A correct answer is worth 5 points.
  • You can get up to 5 bonus points for a speedy answer.
  • Some questions demand more than one answer. You must get every part right.
  • Beware! Wrong answers score 0 points.
  • 🏆 If you beat one of the top 3 scores, you will be invited to apply for the Hall of Fame.
Scoring System

Guru (+)
Hero (+)
Captain (+)
Sergeant (+)
Recruit (+)

Codes for the ⋅ Symbol

The Symbol
Alt CodeAlt 8901
HTML Code⋅
HTML Entity⋅
CSS Code\22C5
Hex Code⋅

How To Insert the ⋅ Symbol

(Method 1) Copy and paste the symbol.

The easiest way to get the ⋅ symbol is to copy and paste it into your document.

Bear in mind that this is a UTF-8 encoded character. It must be encoded as UTF-8 at all stages (copying, replacing, editing, pasting), otherwise it will render as random characters or the dreaded �.

(Method 2) Use the "Alt Code."

If you have a keyboard with a numeric pad, you can use this method. Simply hold down the Alt key and type 8901. When you lift the Alt key, the symbol appears. ("Num Lock" must be on.)

(Method 3) Use the HTML Decimal Code (for webpages).

HTML TextOutput
<b>My symbol: &#8901;</b>My symbol: ⋅

(Method 4) Use the HTML Entity Code (for webpages).

HTML TextOutput
<b>My symbol: &sdot;</b>My symbol: ⋅

(Method 5) Use the CSS Code (for webpages).

CSS and HTML TextOutput
span:after {
content: "\22C5";}
<span>My symbol:</span>
My symbol: ⋅

(Method 6) Use the HTML Hex Code (for webpages and HTML canvas).

HTML TextOutput
<b>My symbol: &#x22C5;</b>My symbol: ⋅
On the assumption that you already have your canvas and the context set up, use the Hex code in the format 0x22C5 to place the ⋅ symbol on your canvas. For example:
JavaScript Text
const x = "0x"+"E9"
ctx.fillText(String.fromCodePoint(x), 5, 5);

(Method 7) Use the Unicode (for various, e.g. Microsoft Office, JavaScript, Perl).

The Unicode for ⋅ is U+22C5. The important part is the hexadecimal number after the U+, which is used in various formats. For example, in Microsoft Office applications (e.g. Word, PowerPoint), do the following:
[Hold down Alt]
[Press x]

(The 22C5 turns into ⋅. Note that you can omit any leading zeros.)
In JavaScript, the syntax is \uXXXX. So, our example would be \u22C5. (Note that the format is 4 hexadecimal characters.)
JavaScript TextOutput
let str = "\u22C5"
document.write("My symbol: " + str)
My symbol: ⋅

You might also like...

Help Us Improve Mathematics Monster

  • Do you disagree with something on this page?
  • Did you spot a typo?
Please tell us using this form.

Find Us Quicker!

  • When using a search engine (e.g., Google, Bing), you will find Mathematics Monster quicker if you add #mm to your search term.

Share This Page

share icon

If you like Mathematics Monster (or this page in particular), please link to it or share it with others.

If you do, please tell us. It helps us a lot!

Create a QR Code

create QR code

Use our handy widget to create a QR code for this page...or any page.

next up:

Dot Minus (∸)

More about Mathematical Symbols

Mathematics is a universal language that is used to describe and understand the intricacies of the universe. At the heart of this language are symbols, concise representations that convey specific meanings and ideas.

Just as letters come together to form words in spoken languages, mathematical symbols combine to form expressions and equations, encapsulating intricate ideas in a compact form. The history of these symbols is as varied as their meanings; some have been in use for centuries while others have been introduced more recently to describe new discoveries and concepts. Whether you are a student, educator, researcher, or simply curious, this list of mathematical symbols will serve as a guide, shedding light on their meanings, origins, and applications.

From the simple plus and minus signs to the more esoteric and complex, each symbol has its unique story and significance.

More Symbols

Full List of Mathematical Symbols