# Dot Product Calculator

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"). X data (comma separated) Y data (comma separated)

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:

$\langle x, y \rangle = \sum_{i=1}^n x_i y_i = x^t \cdot y$

Some uses of the dot product are super neat and practical: The dot product calculator and the angle. Indeed, the dot or inner product also has a strong geometric motivation. Certainly, 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 $$y$$.

### The dot product and the cross product

A related operation for two vectors is the cross product, although it has a different now since its output is a vector and not a scalar.

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