Dot Product Calculator
2D & 3D Vector Analysis
Calculate dot product, angle between vectors, magnitudes, and projections for 2D and 3D vectors.
Vector Input
Vector 1 (v₁)
Vector 2 (v₂)
Dot Product Formula
2D: v₁ · v₂ = x₁×x₂ + y₁×y₂
3D: v₁ · v₂ = x₁×x₂ + y₁×y₂ + z₁×z₂
Key Properties
Commutative: v₁ · v₂ = v₂ · v₁
Distributive: v₁ · (v₂ + v₃) = v₁ · v₂ + v₁ · v₃
Scalar: (cv₁) · v₂ = c(v₁ · v₂)
Orthogonal: v₁ · v₂ = 0
You Might Also Like
Explore more tools in this category
Prime Number Generator
Generate prime numbers in any range using efficient algorithms
Factorial Calculator
Calculate factorials, permutations, and combinations with steps
Perfect Square Calculator
Check if a number is a perfect square and find square roots
Perfect Cube Calculator
Check if a number is a perfect cube and find cube roots
Cube Root Calculator
Calculate cube roots with simplification and step-by-step solutions
RMS Calculator
Calculate Root Mean Square for datasets, AC voltage and current
Acceleration Calculator
Calculate acceleration using velocity, force, distance, or gravity
Dew Point Calculator
Calculate dew point, heat index, humidex, and comfort levels
Earthquake Calculator
Calculate earthquake magnitude, energy, intensity, and compare seismic events