CalculatorMath Calculator

Cross Product Calculator – Free Online Calculator

Advanced Cross Product Calculator

Cross Product Calculator

Features of the Advanced Calculator:

  • User-Friendly Interface:

    • Clean layout with clear labels and placeholders.
    • Responsive design that adapts to different screen sizes.
  • Real-Time Calculation:

    • Computes the cross product instantly when the Solve button is clicked.
  • Input Flexibility:

    • Accepts decimal and negative values.
    • Empty inputs are treated as zero for convenience.
  • Output Precision:

    • Results are displayed with two decimal places. Adjust toFixed(2) in the script for more precision.

Understanding the Cross Product:

The cross product (vector product) of two vectors A and B in three-dimensional space is a vector C that is perpendicular to both A and B. The direction of C is given by the right-hand rule, and its magnitude is equal to the area of the parallelogram formed by A and B.

Mathematical Formula:

A×B=(a2b3a3b2a3b1a1b3a1b2a2b1)\mathbf{A} \times \mathbf{B} = \begin{pmatrix} a_2 b_3 – a_3 b_2 \\ a_3 b_1 – a_1 b_3 \\ a_1 b_2 – a_2 b_1 \\ \end{pmatrix}

Where:

  • a1,a2,a3a_1, a_2, a_3 are the components of vector A.
  • b1,b2,b3b_1, b_2, b_3 are the components of vector B.

How to Use the Cross Product Calculator:

  1. Enter the Components:

    • Input the x,y,zx, y, z components of Vector A in the first set of input fields.
    • Input the x,y,zx, y, z components of Vector B in the second set of input fields.
  2. Calculate:

    • Click the Solve button to compute the cross product.
  3. View the Result:

    • The cross product A×B\mathbf{A} \times \mathbf{B} will be displayed below the button.

Applications of Cross Product:

  • Physics:

    • Calculating torque, angular momentum, and magnetic force.
    • Determining the normal vector to a surface.
  • Engineering:

    • Finding perpendicular vectors in structural analysis.
    • Computing moments and forces in mechanics.
  • Computer Graphics:

    • Calculating normals for lighting and shading.
    • Rotating objects around an axis.

 

How to Use the Cross Product Calculator?

The procedure to use the cross product calculator is as follows:

Step 1: Enter the real numbers in the respective input field

Step 2: Now click the button  “Solve” to get the cross product

Step 3: Finally, the cross product of two vectors will be displayed in the output field

What is Meant by Cross Product?

In Mathematics, the cross product is also known as the vector product, is a binary operation of two vectors in the three-dimensional space. The formula to calculate the cross product of two vectors is given below:

a × b = |a| |b| sin(θ) n

Where

a, b are the two vectors

θ is the angle between two vectors

| | represents the magnitude

n is a unit vector which is at right angles to both the vectors a and b

Shares:

Leave a Reply

Your email address will not be published. Required fields are marked *