➕ Vector Addition Calculator
Calculate sum of two vectors
Vector A
Vector B
How to Use This Calculator
Enter Vector A Components
Input the x, y, and optionally z components of the first vector A.
Enter Vector B Components
Input the x, y, and optionally z components of the second vector B.
Calculate
Press "Calculate Vector Sum" to find A + B (component-wise addition).
Formula
A + B = (A_x + B_x, A_y + B_y, A_z + B_z)
Component-wise addition
Example: A = (3, 4), B = (1, 2)
A + B = (3 + 1, 4 + 2) = (4, 6)
|A + B| = √(4² + 6²) = √52 ≈ 7.21
About Vector Addition Calculator
The Vector Addition Calculator adds two vectors component-wise. Vector addition is performed by adding corresponding components: A + B = (A_x + B_x, A_y + B_y, A_z + B_z).
When to Use This Calculator
- Physics: Add velocity, force, or acceleration vectors
- Engineering: Combine forces and displacements
- Mathematics: Perform vector operations
- Computer Graphics: Add displacement vectors in 3D rendering
- Navigation: Combine velocity or displacement vectors
Understanding Vector Addition
Vector addition is component-wise: add x-components, y-components, and z-components separately. The result is a new vector representing the combined effect.
Frequently Asked Questions
How do I add two vectors?
Add corresponding components: A + B = (A_x + B_x, A_y + B_y, A_z + B_z). This is component-wise addition.
Is |A + B| = |A| + |B|?
Generally no! |A + B| ≤ |A| + |B| (triangle inequality). Equality holds only when A and B point in the same direction. Usually |A + B| < |A| + |B|.
Can I add vectors of different dimensions?
For calculation purposes, you can treat 2D vectors as 3D with z = 0. However, mathematically, vectors of different dimensions belong to different vector spaces.