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vector-algebra

Abstract math for vector algebra in 2D and 3D Euclidean space. USE FOR: implementing vector operations (add, subtract, negate, scalar multiply/divide); dot product and geometric interpretation; 3D cross product; 2D pseudo-cross product (scalar z-component); vector magnitude and normalization; angle between two vectors; linear interpolation; checking zero/unit/finite vectors. 2D is a special case of 3D with z=0. DO NOT USE FOR: quaternion operations (use quaternion-algebra); rotation representations (use 3d-rotation-theory); coordinate system conversions (use coordinate-system-conversions).

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NetFabric/NetFabric.Numerics36 stars(GitHub 36 + cccskills 0)

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Files included (3)

SKILL.md2.5 KB
references/formulas.md2.0 KB
references/numerical-stability.md2.3 KB

SKILL.md (original)

Review the instructions the agent will receive before you install.

Vector Algebra

Point − Point = Vector (displacement). Point + Vector = Point (translation).

Operations (component-wise)

Operation	Formula	Result type
Addition	a + b = (aₓ+bₓ, aᵧ+bᵧ[, a_z+b_z])	Vector
Subtraction	a − b	Vector
Scalar multiply	kv = (kvₓ, kvᵧ[, kv_z])	Vector
Scalar divide	v/k	Vector
Negation	−v = (−vₓ, −vᵧ[, −v_z])	Vector

Magnitude & Normalization

‖v‖  = √(vₓ² + vᵧ² [+ v_z²])        (Euclidean norm)
‖v‖² = vₓ² + vᵧ² [+ v_z²]           (avoid sqrt when comparing)
v̂    = v / ‖v‖                         (unit vector; undefined if ‖v‖ = 0)

Dot Product

a · b = aₓbₓ + aᵧbᵧ [+ a_z b_z] = ‖a‖ ‖b‖ cos θ

a·b = 0 → perpendicular; a·b = ‖a‖‖b‖ → parallel; sign → acute/obtuse.

Cross Product (3D only)

a × b = (aᵧb_z − a_z bᵧ,  a_z bₓ − aₓb_z,  aₓbᵧ − aᵧbₓ)
‖a × b‖ = ‖a‖ ‖b‖ sin θ

Direction: right-hand rule. Anti-commutative: a × b = −(b × a)

2D pseudo-cross (scalar z-component only): aₓbᵧ − aᵧbₓ — positive = CCW, negative = CW.

Angle Between Vectors

θ = arccos(clamp(a·b / (‖a‖‖b‖), −1, 1)) result ∈ [0, π]

Special Vectors

Name	Condition
Zero	‖v‖ = 0
Unit (normalized)	‖v‖ = 1
Basis 2D	UnitX=(1,0), UnitY=(0,1)
Basis 3D	UnitX=(1,0,0), UnitY=(0,1,0), UnitZ=(0,0,1)

Reference Files

File	Load When
references/formulas.md	Projection, triple product, distance formulas, point operations
references/numerical-stability.md	Near-zero normalization, dot cancellation, magnitude comparison

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Install

Install with a command

npx skills add https://github.com/NetFabric/NetFabric.Numerics --skill vector-algebra

Paste it into your terminal and run it (requires Node.js). You can choose which agents to install it for, such as Claude Code or Codex.

Ask your agent

Please install the following Agent Skill.
https://github.com/NetFabric/NetFabric.Numerics/tree/main/.agents/skills/vector-algebra

First review SKILL.md and the bundled files and confirm there is nothing suspicious (such as sending data externally or reading credentials). Then place it in ~/.claude/skills/vector-algebra/ for Claude Code, or ~/.agents/skills/vector-algebra/ for Codex.

Send this text to Claude Code or Codex as is. It checks the contents before installing.

View source on GitHub

Repository: NetFabric/NetFabric.Numerics
Stars: 36
Forks: 1
Category: Documents
License: MIT
Original language: English
Last updated: Aug 10, 2026

A skill is a set of instructions and scripts for an agent. cccskills does not guarantee that skills are safe. Review the contents before you install.