Dot Product Calculator

📐 Vector Calculator

Enter two 3D vectors for dot product calculation

Vector A (x, y, z)

Vector B (x, y, z)

📊 Results

Dot product and vector analysis

A • B = 0

|A| = 0

|B| = 0

Angle θ = 0°

Relationship -

📈 Component Analysis

Vector components comparison

🎯 3D Vector Space

Interactive vector visualization

Drag to rotate • Scroll to zoom
Red: Vector A • Green: Vector B

Understanding Dot Product

The dot product (scalar product) is a fundamental operation in vector mathematics. It produces a scalar value that represents the extent to which two vectors point in the same direction. The dot product has numerous applications in physics, computer graphics, and engineering.

Mathematical Definition

A • B = |A| × |B| × cos(θ)
Or: A • B = (Ax × Bx) + (Ay × By) + (Az × Bz)

Geometric Interpretation

Measures how much one vector extends in the direction of another. Positive when vectors point similarly, negative when opposite.

Applications

Used in physics for work calculations, computer graphics for lighting, and machine learning for similarity measures.

Advanced Dot Product Calculator