**Instructions:** Use this online Dot Product Calculator to compute the dot product for two vectors \(x\) and \(y\). All you have to do is type the data for your vectors \(x\) and \(y\), either in comma or space separated format (For example: “2, 3, 4, 5”, or “3 4 5 6 7”).

## More About the Dot Product

The dot product is an operation conducted for two vectors \(x\) and \(y\), and the result of the operation is a scalar. The formula for the dot product is shown below:

\[ \langle x, y \rangle = \sum_{i=1}^n x_i y_i \]The dot product \(\langle x,y \rangle\) is known by different names, and it is also called, *inner product* or *scalar product*. Essentially, the dot product is matrix product if we consider \(x \in \mathbb{R}^n\) and \(y \in \mathbb{R}^n\), then the dot product is defined as:

The dot or inner product also has a strong geometric motivation. Indeed, an alternative expression for it is

\[ \langle x, y \rangle = \|x\| \|y\| \cos \theta \]where \(\|x\|\) is the norm (length) of \(x\), \(\|y\|\) is the norm (length) of \(y\), and \(\theta\) is the angle between \(x\) and \(y\).

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