Linear Combination Calculator (2D)
The Linear Combination Calculator computes c₁·v₁ + c₂·v₂ for two 2D vectors and two scalars. Enter the scalars and vector components.
Formula
Result = c₁·v₁ + c₂·v₂
- Each vector is scaled by its scalar, then the results are added component-wise.
- Any vector in the plane can be written as a linear combination of two independent vectors.
2(1,0) + 3(0,1)
Inputs
- Scalar c₁: 2
- v₁ x: 1
- v₁ y: 0
- Scalar c₂: 3
- v₂ x: 0
- v₂ y: 1
2(1,0) + 3(0,1) = (2, 3).
Frequently asked questions
What is a linear combination?
A sum of vectors each multiplied by a scalar, such as c₁v₁ + c₂v₂.