Dot & Cross Product Calculator

Vector A

Vector B

Results will appear here

About Dot and Cross Product Calculator

The Dot & Cross Product Calculator is a powerful mathematical tool designed to compute key vector operations quickly and accurately. It helps users calculate the dot product, cross product, angle between vectors, and unit vectors in both 2D and 3D space. These operations are fundamental in linear algebra, physics, engineering, and computer graphics.

Vectors are quantities that have both magnitude and direction. Understanding how vectors interact is essential for solving real-world problems involving forces, motion, and spatial relationships. This calculator simplifies complex vector calculations into instant results.

Key Calculations Performed

Dot Product: Measures how much two vectors point in the same direction.
Formula: A · B = AxBx + AyBy + AzBz

Cross Product: Produces a vector perpendicular to both vectors.
Formula: A × B = (AyBz − AzBy, AzBx − AxBz, AxBy − AyBx)

Angle Between Vectors: Determines orientation using:
θ = cos⁻¹[(A · B) / (|A||B|)]

Unit Vector: Gives direction of vector with magnitude 1.

How to Use

Enter the components of Vector A and Vector B. Click the calculate button to instantly get all results including dot product, cross product, angle, and unit vectors.

Example

Vector A = (1, 2, 3)
Vector B = (4, 5, 6)

Dot Product = 32
Cross Product = (-3, 6, -3)

Applications

These vector operations are widely used in physics to calculate work done, torque, and force direction. Engineers use them in mechanics and structural analysis. In computer graphics, they help determine lighting, shading, and 3D transformations. Machine learning and data science also use vector operations for similarity calculations.

This calculator is ideal for students, teachers, and professionals preparing for exams or solving complex problems. It improves accuracy, saves time, and enhances conceptual understanding of vector mathematics.