Convert OnlineConvertOnline
  1. Convert Online›
  2. Physics›
  3. Vector›
  4. Vector Dot Product Calculator

Vector Dot Product Calculator

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

\( \vec{a}\cdot\vec{b} = a_{1} \cdot b_{1} + a_{2} \cdot b_{2} + a_{3} \cdot b_{3} \)

= \( \vec{x} \) + \( \vec{y} \) + \( \vec{z} \)
= \( \vec{x} \) + \( \vec{y} \) + \( \vec{z} \)




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:

  1. Multiply the corresponding components of the vectors.
  2. Sum the products obtained in the previous step.
  3. 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:

  1. Multiply the corresponding components:

    \( \vec{a} \cdot \vec{b} = a_1 \cdot b_1 + a_2 \cdot b_2 + a_3 \cdot b_3 \)

  2. Add the products:

    \( \vec{a} \cdot \vec{b} = 2 \times 5 + 3 \times 6 + 4 \times 7 \)

  3. 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.