A·B

Dot Product 3D

Scalar Projection Lab

Scalar Analytics

Acute (A·B > 0)

Vector A:

[ 3.0, 1.5, 0.0 ]

Vector B:

[ 2.5, 0.0, 2.0 ]

Scalar Dot Product (A · B):

+7.50

Component Form: Ax·Bx + Ay·By + Az·Bz

= (3.0)(2.5) + (1.5)(0.0) + (0.0)(2.0)

= 7.50 + 0.00 + 0.00 = 7.50

Geometric Form: |A| · |B| · cos(θ)

= (3.35) · (3.20) · cos(45.6°)

Magnitude |A|

3.35

Magnitude |B|

3.20

Scalar Proj

+2.34

Angle (θ): 45.6° (0.80 rad)

Simulation Settings

Geometric Presets

Vector A Components

Vector B Components

Projection Direction

Projection Segment Color

Vector Thickness

Visual Layers Orthogonal Projection Visualizer Right-Angle (Perpendicular) Symbol Angle Arc & θ Dimension 3D Floating Text Tags (A, B, θ) Coordinate Axes (+X, +Y, +Z) Floor Reference Grid Dotted Floor Drop Lines

Quick Presentation Tips:

• Press 'H': Completely hide all written formulas, numbers, and tags for clean diagramming.

• Left Drag: Orbit camera in 3D around the vectors.

• Scroll: Zoom in/out smoothly.

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