2D Linear Combination Calculator
Math
2D Linear Combination with stated conventions, validation and a worked example.
Formula
w=αu+βv
- Use the units shown beside each field.
- Results update automatically whenever you change an input.
- Displayed values use up to four decimal places, or scientific notation for very small or large numbers. Calculations use standard floating-point arithmetic; exact integer and fraction tools identify their own precision rules.
- Two-dimensional real vectors with explicit coefficients.
Example Calculation
Example inputs
- Vector u x: 1
- Vector u y: 2
- Vector v x: 3
- Vector v y: 4
- Coefficient α: 2
- Coefficient β: -1
2(1,2)−(3,4)=(−1,0).
Method references
Frequently asked questions
How do I use this calculator?
Enter vector u x, vector u y, vector v x, vector v y, coefficient α, coefficient β. The result updates automatically. Use Reset to restore the example values.
What method does it use?
w=αu+βv. Two-dimensional real vectors with explicit coefficients.
Why might a rounded result differ?
The calculation keeps full numeric precision internally, then rounds the displayed result. Rounding intermediate steps by hand can produce a slightly different answer.
Are my inputs saved online?
No. This calculator processes your inputs in your browser. A recently used list stores only calculator names on this device, not your entered values.
Check the assumptions and units before using this result. Read about calculation methods.