Vector Math Calculator (2D & 3D)
Vector Math Calculator (2D & 3D): Calculates scalar dot product A·B, vector cross product A×B, and Euclidean norms ||A||, ||B||.
About this vector math calculator (2d & 3d)
Vector Math Calculator (2D & 3D) — browser-based utility.
How this tool works
Calculation and parameter relationship: dot=Σaᵢbᵢ; cross=(a₂b₃−a₃b₂,a₃b₁−a₁b₃,a₁b₂−a₂b₁)
- Select “Raw JSON / Advanced” and paste the sample input.
- Click “Run locally”.
- Compare “Raw Output Data” with the example; revise inputs when an error is shown.
Worked example
Scenario: Compute dot product, cross product, and norms of two 3D vectors.
Sample input:
Processing: Sum component products, form the 3D determinant cross product, then apply Math.hypot to each vector.
Illustrative output:
Limits and verification
Parameter domains and units: a,b ∈ ℝ² ∪ ℝ³; dim(a) = dim(b); dim(a) = 2 ⇒ cross = null. Results use binary64 floating-point numbers unless BigInt is stated. Result cards show up to 10 significant digits; raw output retains the serialized value. A null ratio means the model has no meaningful finite value for that ratio; it is not zero.
Examples demonstrate an expected workflow; they do not prove every input or every branch of an external specification. Check important results with an independent source before using them for money, security, compliance, safety, or irreversible file changes.
Browser processing boundary
Tool input is processed by code running in the browser and is not intentionally sent to a CZOA processing API. The page can still request ordinary site assets, analytics, or advertising when those services are enabled. Browser extensions and managed-device software remain outside this tool's control.
Relevant references
These references govern or help explain the format, protocol, or calculation used here. Listing a reference does not claim certification or complete implementation of every optional feature.
- NIST Digital Library of Mathematical Functions, §1.2 — Elementary Algebra
- ECMAScript 2026, §6.1.6.1 Number Type
Content owner: CZOA Tools · Last reviewed: 2026-09-15 · Review methodology
How to use it
- Select “Raw JSON / Advanced” and paste the sample input.
- Click “Run locally”.
- Compare “Raw Output Data” with the example; revise inputs when an error is shown.
Frequently asked questions
How does the vector calculator compute dot, cross, and norms?+
It accepts matching 2D or 3D arrays. It sums coordinate products for dot, uses the three-component determinant formula for 3D cross, and Math.hypot for each norm.
Which JSON input shape is accepted?+
Provide matching a and b arrays with length two or three. The verified vector is {"a":[1,2,3],"b":[4,5,6]}.
What validation and numerical limits apply?+
Other dimensions or mismatched lengths fail. Outputs use JavaScript Number binary64; a 2D input returns cross as null. This is vector arithmetic, not a physics simulation or coordinate-system conversion.
What result does the worked example produce?+
The tool processed {"a":[1,2,3],"b":[4,5,6]} locally and returned dot 32, cross [-3,6,-3], normA 3.741657386773941, and normB 8.774964387392123.