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Vector Addition Calculator

Online vector addition: add two vectors by the triangle/parallelogram rule, component by component.

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a+b=(x₁+x₂,y₁+y₂)
Vector a
x
y
Vector b
x
y

📖 Tutorial | Addition

1. Definition
Vector addition follows the triangle/parallelogram rule; in coordinates a+b=(x₁+x₂,y₁+y₂).
2. Formula & Notation
a,bComponents
3. Properties & Laws
  • Commutative;
  • Associative;
  • a+0=a;
  • Place head to tail.
4. Steps
  1. Enter two vectors;
  2. Click "Add";
  3. Or click "Load Example".
5. Worked Examples
Example: (1,2)+(3,4): (4,6).
6. Common Pitfalls
Match components;
Head to tail;
Opposites sum to zero.

❓ FAQ | Addition

Rule?
Triangle.
Components?
Add.
Laws?
Commutative.
Opposite?
Zero.
Example?
(4,6).
Geometry?
Head to tail.