Cross Product Calculator
Multiply the magnitudes of two vectors and the sine of the angle between them to find the cross product.
The Cross Product Calculator computes the vector perpendicular to two given vectors in 3D space, along with its magnitude and direction.
This is useful in physics, engineering, and mathematics to determine areas of parallelograms, torque, or rotational forces. The cross product is central to calculations involving vector fields, angular momentum, and 3D transformations, offering precise solutions for vector-related problems.
Formula:
A × B = |A| |B| sinθ
| Variable | Definition | Units |
|---|---|---|
| A × B | Cross product result vector | Vector units |
| θ | Angle between vectors A and B | Degrees/Radians |
Solved Calculations:
Example 1: Cross product of vectors A = (3, 4, 5) and B = (1, 2, 3) with θ = 90°
| Step | Value | Explanation |
|---|---|---|
| Magnitude of A ( | A | ) |
| Magnitude of B ( | B | ) |
| sinθ | 1.0 | Sin(90°) = 1 |
| Cross Product Magnitude | 26.44 |
Example 2: Cross product of A = (2, 3, 4) and B = (4, 5, 6) with θ = 45°
| Step | Value | Explanation |
|---|---|---|
| Magnitude of A ( | A | ) |
| Magnitude of B ( | B | ) |
| sinθ | 0.707 | Sin(45°) = 0.707 |
| Cross Product Magnitude | 33.41 |
What is the Cross Product Calculator?
The Cross Product Calculator is a precise tool designed to compute the cross product of two vectors in 2D or 3D space. This calculation is vital in physics, engineering, and mathematics for determining vector orthogonality, finding the area of parallelograms formed by vectors, or calculating torque in mechanical systems.
By inputting the components of two vectors, this calculator provides the resulting vector and its magnitude. It also helps visualize the orthogonality of the resulting vector relative to the input vectors, making it an essential aid for understanding vector operations.
This tool streamlines complex computations, saving time and ensuring accuracy in results. Its applications include solving physics problems, determining surface normals in computer graphics, and analyzing forces in engineering designs.
Final Words:
Ultimately, the Cross Product Calculator is a valuable asset for professionals and students alike, offering quick and reliable solutions for vector cross products across diverse fields of study and applications.
