Vector Algebra
SkillMonitoring & opsAbstract 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).
Available today. Use it from your connected AI after setup.
No other account needed.
Connect ahel once, and every AI you use reads what you have installed.
Then ask your AI: use the Vector Algebra skill
What this skill tells your AI
The instructions your AI receives, as published by netfabric/netfabric.numerics in .agents/skills/vector-algebra/SKILL.md and read by ahel’s review.
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 |
Signals
- GitHub stars
- 36
- Forks
- 1
- Last commit
- Aug 2026
Advanced
- Catalog kind
- skill
- Gateway key
vector-algebra- Source
- github.com/netfabric/netfabric.numerics