Vector Subtraction Calculator
Subtract two 2D or 3D vectors and find the magnitude of the difference.
How it works
- 1Enter the x, y (and optionally z) components for vector a and vector b.
- 2Each component of b is subtracted from the matching component of a to form the difference vector a − b.
- 3The magnitude |a − b| is computed as √(Σ(aᵢ − bᵢ)²), giving the straight-line distance between the two tip points.
Use cases
- Finding the displacement vector between two positions in 2D or 3D space.
- Computing the relative velocity of one object with respect to another in physics simulations.
- Measuring the Euclidean distance between two data points represented as vectors.
Frequently asked questions
Is vector subtraction commutative?
No. a − b and b − a point in opposite directions; only their magnitudes are equal.
What does the magnitude |a − b| represent?
It equals the Euclidean distance between the tips of the two vectors when both are placed at the same origin.
Can I subtract vectors of different dimensions?
Mathematically, only vectors of the same dimension should be subtracted. This calculator treats any missing component as 0, consistent with standard embedding conventions.
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