Dot Product Calculator
Enter your vectors as comma-separated numbers, and we'll provide a detailed step-by-step solution showing how to find the dot product, which measures how parallel two vectors are and is used in physics, engineering, and computer graphics.
About Dot Products
The dot product of two vectors is the sum of the products of their corresponding components.
Key properties:
- Commutative: a·b = b·a
- Distributive: a·(b + c) = a·b + a·c
- The dot product of perpendicular vectors is 0
- For parallel vectors, a·b = |a||b|