Dot Product Calculator
Calculate the dot product of two 3D vectors quickly and easily. Perfect for physics, engineering, and mathematical calculations.
Result: 32
Understanding Dot Products
The dot product (also known as scalar product) is a fundamental operation in vector algebra that takes two vectors and returns a single number. For two vectors a = (a₁, a₂, a₃) and b = (b₁, b₂, b₃), the dot product is calculated as:
a · b = a₁b₁ + a₂b₂ + a₃b₃
Applications
- Physics: Work calculations (Force × Distance)
- Computer Graphics: Light intensity calculations
- Machine Learning: Feature similarity measures
- Engineering: Structural analysis