What Is the Dot Product?
The dot product (scalar product) of two vectors gives a single number. For vectors A and B:
A · B = AxBx + AyBy + AzBz
A · B = |A| |B| cos(θ)
Interpretation
- Positive dot product: vectors point in similar directions (angle < 90°)
- Zero dot product: vectors are perpendicular (angle = 90°)
- Negative dot product: vectors point in opposite directions (angle > 90°)