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2D Vector Resultant Calculator — result sheet
Add two two-dimensional vectors and calculate the resultant components, magnitude, dot product, and cross-product z component.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: R = A+B; |R| = √(Rₓ²+Rᵧ²); A·B = AₓBₓ+AᵧBᵧ; (A×B)z = AₓBᵧ-AᵧBₓ.
Vector addition is performed component by component. The dot product measures alignment, while the two-dimensional cross-product z component records signed turning area.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Vector A x — minimum -1000000000; maximum 1000000000
- Vector A y — minimum -1000000000; maximum 1000000000
- Vector B x — minimum -1000000000; maximum 1000000000
- Vector B y — minimum -1000000000; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Vector A x | 3 |
| Vector A y | 4 |
| Vector B x | -1 |
| Vector B y | 2 |
Resultant: (2, 6); magnitude: about 6.325; dot product: 5; cross z: 10.
Assumptions and limits
- Both vectors are represented in the same two-dimensional Cartesian coordinate system and units.
- The cross-product result is the z component of the corresponding three-dimensional cross product with zero z inputs.
- No unit conversion or coordinate projection is applied.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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