3D Right-Handed Coordinate System & Vector Visualizer

Vector Analytics & Right-Hand Rule

High-Contrast Educational Display

Vector Representation

|V⃗| = 5.39

V⃗ = 3.0î + 4.0ĵ + 2.0k̂

Magnitude Formula: √(Vx² + Vy² + Vz²) √(9 + 16 + 4) = 5.39

Direction Angles & Cosines cos²α + cos²β + cos²γ = 1

α (with X-axis)

56.1°

cos α = 0.56

β (with Y-axis)

42.1°

cos β = 0.74

γ (with Z-axis)

68.2°

cos γ = 0.37

Right-Hand Convention Status

Curl fingers of right hand from +X (î) to +Y (ĵ); out-stretched thumb defines +Z (k̂) orientation (î × ĵ = k̂).

Parameters & Customization

Coordinate Presets Standard Configurations

Vector V⃗ Components (x, y, z)

Vx (î axis)

Vy (ĵ axis)

Vz (k̂ axis)

Visual Layers & Geometry 3D Projection Box & Droplines Right-Hand Curl Arc (î → ĵ → k̂) Direction Angle Arcs (α, β, γ) Unit Basis Vectors (î, ĵ, k̂) 3D Floating Text Labels Coordinate Planes (XY, YZ, XZ) Ground Reference Grid

Geometry Sizing

Vector Thickness:

Axis Length:

Plane Opacity:

Axis Colors

X-Axis

Y-Axis

Z-Axis

Notification