Vector Addition Calculator
Add two or more vectors component-wise in any dimension and show the resultant.
Inputs
A + B
[5, 7, 9]
Magnitude of Result
12.449900
Step by step
Vector A
= [1, 2, 3]
Vector B
= [4, 5, 6]
A + B
= [5, 7, 9]
||A + B||
= 12.4499
How it works
Vector addition sums corresponding components: (A+B)ᵢ = Aᵢ + Bᵢ. Both vectors must have the same dimension. The resultant's magnitude is computed as the Euclidean norm.
Formula
Component-wise Addition
(A + B)ᵢ = Aᵢ + Bᵢ
- A
- First vector
- B
- Second vector
Frequently Asked Questions
Do vectors need to be the same dimension?
Yes. You can only add vectors of the same dimension — each component is summed with its counterpart.
Is vector addition commutative?
Yes. A + B = B + A, just like scalar addition.