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Vector Subtraction Calculator

Online vector subtraction: a−b=a+(−b), component by component.

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a−b=a+(−b)
Vector a
x
y
Vector b
x
y

📖 Tutorial | Subtraction

1. Definition
a−b=a+(−b), in coordinates (x₁−x₂,y₁−y₂); geometrically it points from the endpoint of b to that of a.
2. Formula & Notation
−bOpposite vector
3. Properties & Laws
  • Add the opposite;
  • a−a=0;
  • Join endpoints;
  • Not commutative.
4. Steps
  1. Enter two vectors;
  2. Click "Subtract";
  3. Or click "Load Example".
5. Worked Examples
Example: (5,6)−(1,2): (4,4).
6. Common Pitfalls
Order matters;
Points from b to a;
Subtract components.

❓ FAQ | Subtraction

Components?
Subtract.
Geometry?
Endpoints.
With addition?
Opposite.
a−a?
Zero.
Example?
(4,4).
Order?
Matters.