Calculator for the scalar product or dot product of 2-dimensional vectors
To calculate the vector dot product enter the vectors, then click the 'Calculate' button. Empty elements are counted as 0.
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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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