Vector Resolver Calculator
Resolve vectors into components, calculate resultant vectors, and analyze dot and cross products in both 2D and 3D space with visual representation.
Formulas Used
- 2D Components:
- x = V cos(θ)
- y = V sin(θ)
- 3D Components:
- x = V cos(θy) cos(θx)
- y = V cos(θy) sin(θx)
- z = V sin(θy)
- Magnitude:
- |V| = √(x² + y² + z²)
- Resultant Vector:
- R = ΣV
- Dot Product:
- A · B = AxBx + AyBy + AzBz
- Cross Product:
- A × B = (AyBz − AzBy, AzBx − AxBz, AxBy − AyBx)
Vector Analysis Details
- - Vectors can be defined using magnitude & angle or components.
- - Automatically converts between polar and Cartesian forms.
- - Supports both 2D and 3D vector systems.
- - Resultant vector is calculated by summing all components.
- Dot Product Insights:
- - Measures alignment between vectors.
- - Positive → same direction
- - Zero → perpendicular
- - Negative → opposite direction
- Cross Product Insights:
- - Produces a vector perpendicular to both inputs.
- - Only defined in 3D space.
- - Direction follows right-hand rule.
- Visualization:
- - 2D mode shows vectors on a Cartesian plane.
- - 3D mode uses Three.js for spatial visualization.
- - Resultant vector is highlighted for clarity.
- Notes:
- - Maximum 3 vectors supported for clarity.
- - Angles can be in degrees or radians.
- - Units are consistent across all calculations.