ToolHub

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.

Vector 1

Calculation History