Dot product of a vector

This function calculates the scalar or dot product of 3-dimensional vectors. To perform the calculation, enter the vectors and click the Calculate button. Empty fields are counted as 0.

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

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