ConvertOnline

Image

Audio

Video

Document

Color

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

{
  "topic": "vector-dot-product",
  "formula_mathjax": "\\( \\vec{a}\\cdot\\vec{b} = a_{1} \\cdot b_{1} + a_{2} \\cdot b_{2} + a_{3} \\cdot b_{3} \\)",
  "formula": " a1 * b1 + a2 * b2 + a3 * b3 ",
  "input_pre_msg": "Enter the inputs and click on Calculate button. Empty inputs are considered 0.",
  "type": "Calculate",
  "title": "Vector Dot Product Calculator",
  "description": "Calculate the vector dot product of two vectors with our Vector Dot Product Calculator. Input the vector components to get instant results. Ideal for students, teachers, and professionals in physics and engineering.",
  "category": "Vector",
  "template": "physics",
  "content": "<h2>What is Vector Dot Product</h2><p>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.</p><p>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.</p><h3>Steps to Calculate the Vector Dot Product</h3><p>Here are the steps to calculate the vector dot product of two vectors:</p><ol class=\"steps\">    <li>Multiply the corresponding components of the vectors.</li>    <li>Sum the products obtained in the previous step.</li>    <li>The resulting sum is the vector dot product of the vectors.</li></ol><h3>Example</h3><p>Let's take an example to illustrate the process. Suppose we have two vectors <strong>a</strong> and <strong>b</strong>:</p><p>\\(\\vec{a} = (a_1, a_2, a_3)\\) = (2, 3, 4)</p><p>\\(\\vec{b} = (b_1, b_2, b_3)\\) = (5, 6, 7)</p><p>To find the vector dot product \\(\\vec{a} \\cdot \\vec{b}\\), we follow these steps:</p><ol class=\"steps\">    <li>Multiply the corresponding components:<p>\\( \\vec{a} \\cdot \\vec{b} = a_1 \\cdot b_1 + a_2 \\cdot b_2 + a_3 \\cdot b_3 \\)</p></li>    <li>Add the products:<p>\\( \\vec{a} \\cdot \\vec{b} = 2 \\times 5 + 3 \\times 6 + 4 \\times 7 \\)</p></li>    <li>Calculate the sum: <p>\\( \\vec{a} \\cdot \\vec{b} = 10 + 18 + 28 = 56 \\)</li></ol><p>The sum is 56.</p><p>Therefore, the vector dot product of \\(\\vec{a} = (2, 3, 4)\\) and \\(\\vec{b} = (5, 6, 7)\\) is 56.</p>"
}