Vector geometry workspace

Supply matching two- or three-dimensional u and v vectors, with each component within ±1000000. Exact results include sum, difference, dot product, squared lengths, projection of u onto v and the perpendicular component; three dimensions also include the cross product. Projection onto zero v and angles involving a zero vector are undefined. Lengths and angles are approximate. Two-dimensional diagrams use equal axis scales; three-dimensional diagrams are explicitly isometric projections and do not preserve lengths or angles. All processing stays on your device. Paste JSON with dot decimals; quote exact fractions and large integers. Input is limited to 100,000 characters and 100 digits per scalar. Exact results use reduced fractions, with a 1,024-digit and 200,000-step arithmetic bound. Enumeration is limited to 10,000 complete results and 1,000,000 search steps; exceeding a bound returns an error, not a partial answer. Geometry uses floating-point approximations. JSON and typed JSON Pointer CSV retain the complete input, results, constraints and worked steps. Reports are limited to 4,000,000 JSON and 8,000,000 CSV characters. Each calculation uses a disposable worker with a 10-second timeout. Search and sort the first 200 preview rows. Copy result copies the summary. Download JSON or CSV for every result and worked step. Geometry tools also provide a downloadable SVG diagram. Supply matching two- or three-dimensional u and v vectors, with each component within ±1000000. Exact results include sum, difference, dot product, squared lengths, projection of u onto v and the perpendicular component; three dimensions also include the cross product. Projection onto zero v and angles involving a zero vector are undefined. Lengths and angles are approximate. Two-dimensional diagrams use equal axis scales; three-dimensional diagrams are explicitly isometric projections and do not preserve lengths or angles. All processing stays on your device. Paste JSON with dot decimals; quote exact fractions and large integers. Input is limited to 100,000 characters and 100 digits per scalar. Exact results use reduced fractions, with a 1,024-digit and 200,000-step arithmetic bound. Enumeration is limited to 10,000 complete results and 1,000,000 search steps; exceeding a bound returns an error, not a partial answer. Geometry uses floating-point approximations. JSON and typed JSON Pointer CSV retain the complete input, results, constraints and worked steps. Reports are limited to 4,000,000 JSON and 8,000,000 CSV characters. Each calculation uses a disposable worker with a 10-second timeout. Up to 100,000 characters. Review the settings before running.