3D Vector Scalar Multiplication Visualizer

Vector Transformation

High-Contrast Formula Panel

Geometric Behavior

Magnitude stretched by factor of 2.0, direction unchanged

ORIGINAL VECTOR v⃗

|v⃗| = 3.74

v⃗ = [ 2.0 î, 1.0 ĵ, 3.0 k̂ ]

SCALAR FACTOR (k) k = +2.0

-5 +5

SCALED RESULT w⃗ = k · v⃗

|w⃗| = |k||v⃗| = 7.48

w⃗ = [ 4.0 î, 2.0 ĵ, 6.0 k̂ ]

Formula: w⃗ = (k · v_x)î + (k · v_y)ĵ + (k · v_z)k̂

Parameters & Customization

Scalar Presets (k) Standard Cases

Original Vector v⃗

Scaled Vector w⃗ (Color & Display)

3D Spatial Arrangement:

Visual Layers Infinite Line of Action (Dashed Collinear) Floor Drop Lines (3D Coordinates) 3D Vector Labels (v⃗, w⃗) Coordinate Axes (+X, +Y, +Z) Ground Reference Grid

Vector Thickness:

Individual Element Toggles:

Background Color

Notification