# Vector Dot Product Calculator

Enter the inputs and click on Calculate button. Empty inputs are considered 0.

## What is Vector Dot Product

The Vector Dot Product, also known as the Dot Product, is a way of multiplying two vectors to get a scalar quantity. This product provides a measure of how much one vector goes in the direction of another.

Vectors in three-dimensional space can be represented as \(\vec{v} = (v_1, v_2, v_3)\), where \(v_1\), \(v_2\), and \(v_3\) are the components of the vector along the x, y, and z axes, respectively.

### Steps to Calculate the Vector Dot Product

Here are the steps to calculate the vector dot product of two vectors:

- Multiply the corresponding components of the vectors.
- Sum the products obtained in the previous step.
- The resulting sum is the vector dot product of the vectors.

### Example

Let's take an example to illustrate the process. Suppose we have two vectors **a** and **b**:

\(\vec{a} = (a_1, a_2, a_3)\) = (2, 3, 4)

\(\vec{b} = (b_1, b_2, b_3)\) = (5, 6, 7)

To find the vector dot product \(\vec{a} \cdot \vec{b}\), we follow these steps:

- Multiply the corresponding components:
\( \vec{a} \cdot \vec{b} = a_1 \cdot b_1 + a_2 \cdot b_2 + a_3 \cdot b_3 \)

- Add the products:
\( \vec{a} \cdot \vec{b} = 2 \times 5 + 3 \times 6 + 4 \times 7 \)

- Calculate the sum:
\( \vec{a} \cdot \vec{b} = 10 + 18 + 28 = 56 \)

The sum is 56.

Therefore, the vector dot product of \(\vec{a} = (2, 3, 4)\) and \(\vec{b} = (5, 6, 7)\) is 56.