Subtract two vectors component-wise in 2D or 3D, with magnitude and step-by-step work.
Dimensions
Vector 1
Vector 2
Component-wise subtraction
Each component of vector 2 is subtracted from the corresponding component of vector 1. The result preserves the original dimensionality.
Order matters
Vector subtraction is not commutative: v1 - v2 produces a different result than v2 - v1. The direction of the resulting vector is reversed when the operand order changes.
Result
(5, 7) − (2, 3) = (3, 4)
Step-by-step
x: 5 − 2 = 3
y: 7 − 3 = 4
Geometric interpretation
The result vector points from the tip of v2 to the tip of v1 when both vectors share the same origin.
Also in Linear Algebra
Linear Algebra
A vector subtraction calculator computes v₁ − v₂ by subtracting corresponding components. It returns the result vector and its magnitude.
To subtract vectors, subtract each component: (a₁−b₁, a₂−b₂, a₃−b₃). The result points from the tip of v₂ to the tip of v₁.
Unlike addition, vector subtraction is not commutative: v₁ − v₂ ≠ v₂ − v₁ (the results are negatives of each other).
Frequently asked questions
Yes — v₁ − v₂ is equivalent to v₁ + (−v₂), where −v₂ negates each component of v₂.
The difference vector v₁ − v₂ points from the tip of v₂ to the tip of v₁ when both are drawn from the same origin.
Related
These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.
Add multiple 2D or 3D vectors component-wise and find the resultant vector with magnitude.
Perform vector operations including addition, subtraction, dot product, cross product, and scalar multiplication.
Calculate the magnitude of a 2D or 3D vector with squared magnitude, unit vector, and direction angles.
Calculate the dot product of two vectors in 2D or 3D, with angle and orthogonality detection.
