Vector Dot Product Calculator
Online calculator for calculating the vector dot product
The calculator on this page calculates the vector dot product with 2, 3 or 4 elements.
To calculate, select the number of elements (3 is the default). Enter the values of the two vectors. Then click on the 'Calculate' button
The value 0 is assumed for empty fields.
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Formulas and examples
This section describes how to calculate the dot product of two vectors.
In contrast to vector multiplication, the result of multiplication to the vector dot product is not a vector, but a real number (scalar product). The dot product is a mathematical combination that assigns a number (scalar) to two vectors.
For two vectors\(\overrightarrow{x}=\left[\matrix{x_1\\⋮\\x_n}\right]\) and \(\overrightarrow{y}=\left[\matrix{y_1\\⋮\\y_n}\right]\) one defines the dot product as \(\displaystyle \overrightarrow{x}·\overrightarrow{y} \)
The individual elements of the vectors are multiplied with each other and the products added. The sum of the addition is the dot product of the vectors.
Dot product \(\displaystyle= x_1·y_1 + ⋯ + x_n·y_n\)
Example
Vectors with 3 elements
\(\displaystyle\overrightarrow{x}=\left[\matrix{1\\2\\3}\right]\) \(\displaystyle\overrightarrow{y}=\left[\matrix{4\\5\\6}\right]\)\(\displaystyle\overrightarrow{x}·\overrightarrow{y}= 1·4+2·5+3·6\) \(\displaystyle=4+10+18=32\)
Vectors with 2 elements
\(\displaystyle\overrightarrow{x}=\left[\matrix{1\\2}\right]\) \(\displaystyle\overrightarrow{y}=\left[\matrix{4\\5}\right]\)\(\displaystyle\overrightarrow{x}·\overrightarrow{y}= 1·4+2·5\) \(\displaystyle=4+10=14\)
Vector Functions
Addition • Subtraction • Multiplication • Scalar Multiplication • Division • Scalar Division • Dot Product • Cross Product • Interpolation • Distance • Distance Squaret • Normalization • Reflection • Magnitude • Squared-Magnitude • Triple-Product
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