Dot product of a vector

Online calculator for calculating the scalar product or dot product of two vectors with 2 elements

Calculate vector dot product


Vector dot product calculator

Vector 1Vector 2Result
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More vector functions for 2 elements

Addition
Subtraction
Multiplication
Scalar Multiplication
Division
Scalar-Division
Scalar Product
Interpolation
Distance
Distance Square
Normalization
Length

Vector functions for 3 or 4 elements

Description of the vector dot product


In contrast to vector multiplication, the result of multiplication to the vector scalar product is not a vector, but a real number (scalar product).

The individual elements of the vectors are multiplied with one another and the products added. The sum of the addition is the scalar product of the vector.

For two vectors \(\overrightarrow{x}=\left[\matrix{x_1\\⋮\\x_n}\right]\) and \(\overrightarrow{y}=\left[\matrix{y_1\\⋮\\y_n}\right]\)
the scalar product is defined as \(\overrightarrow{x}·\overrightarrow{y}= x_1·y_1 + ⋯ + x_n·y_n\)

Example

\(\overrightarrow{x}=\left[\matrix{1\\2\\3}\right]\)     \(\overrightarrow{y}=\left[\matrix{4\\5\\6}\right]\)     \(\overrightarrow{x}·\overrightarrow{y}= 1·4+2·5+3·6=4+10+18=32\)

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