Understand the subject
What does vector addition or subtraction do?
A vector lists directed components. Addition combines matching components; subtraction measures the directed change from one vector to another.
Use it to combine displacements, velocities, forces, or any quantities with the same coordinate system.
See the structure
What the calculation is doing
1234
same positions5678
(u±v)ᵢ=uᵢ±vᵢWorked interpretation
Read the result in context
(u±v)ᵢ=uᵢ±vᵢ
Interpret with care
Important boundary
Vectors must use the same dimension and the same coordinate convention.
Use the Matrix Calculator to experiment with small exact matrix operations before applying a more specialized route.
Quick guide
How to use this calculator
- Choose addition or subtraction.
- Give a and b the same number of components.
- Enter every component and read the exact vector.
Calculation method
Combine matching components
Vector addition and subtraction act component by component while preserving the order of the coordinates.
Worked example
Add two 3D vectors
Add a = ⟨1,2,3⟩ and b = ⟨4,−1,2⟩.
a + b = ⟨5,1,5⟩
Supported inputs
Precision and limits
Vector size
General vectors may contain 2–8 components; three-dimensional products require exactly three.
Entry precision
Each signed decimal may contain up to 30 digits and 15 decimal places.
Square roots
Squared magnitudes remain exact. Irrational roots and normalized components are explicitly labelled approximations.
