# Dot Product Calculator

## Calculator Use

- Enter two or more vectors and click Calculate to find the dot product.
- Define each vector with parentheses "( )", square brackets "[ ]", greater than/less than signs "< >", or a new line.
- Separate terms in each vector with a comma ",". The number of terms must be equal for all vectors.
- Vectors may contain integers and decimals, but not fractions, functions, or variables.

## About Dot Products

In linear algebra, a dot product is the result of multiplying the individual numerical values in two or more vectors. If we defined vector a as <a_{1}, a_{2}, a_{3}.... a_{n}> and vector b as <b_{1}, b_{2}, b_{3}... b_{n}> we can find the dot product by multiplying the corresponding values in each vector and adding them together, or (a_{1} * b_{1}) + (a_{2} * b_{2}) + (a_{3} * b_{3}) .... + (a_{n} * b_{n}). We can calculate the dot product for any number of vectors, however all vectors must contain an equal number of terms.

### Example

Find a ⋅ b when a = <3, 5, 8> and b = <2, 7, 1>

a ⋅ b = (a_{1} * b_{1}) + (a_{2} * b_{2}) + (a_{3} * b_{3})

a ⋅ b = (3 * 2) + (5 * 7) + (8 * 1)

a ⋅ b = 6 + 35 + 8

a ⋅ b = 49

## Further Reading

- Khan, Salman "Vector dot product and vector length",
*The Khan Academy,*Vector Dot Product and Vector Length.

**Cite this content, page or calculator as:**

Furey, Edward "Dot Product Calculator" at https://www.calculatorsoup.com/calculators/algebra/dot-product-calculator.php from CalculatorSoup,
*https://www.calculatorsoup.com* - Online Calculators

Last updated: August 17, 2023