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:

$$\mathbf{A} \times \mathbf{B} = \begin{pmatrix} a_2 b_3 – a_3 b_2 \\ a_3 b_1 – a_1 b_3 \\ a_1 b_2 – a_2 b_1 \\ \end{pmatrix}$$

Where:

• $a_1, a_2, a_3$ are the components of vector A.
• $b_1, b_2, b_3$ are the components of vector B.

How to Use the Cross Product Calculator:

1. Enter the Components:

   • Input the $x, y, z$ components of Vector A in the first set of input fields.
   • Input the $x, y, z$ 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 $\mathbf{A} \times \mathbf{B}$ 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.