# Vector Subtraction Calculator

> Calculate and visualize vector subtraction in 2D and 3D space

**Category:** Math
**Keywords:** vector, subtraction, calculator, math, 2d, 3d, magnitude, component, linear algebra, physics
**URL:** https://complete.tools/vector-subtraction-calculator

## How it calculates

The formula for vector subtraction is given by: 

**For 2D Vectors:** 
If **A = (Ax, Ay)** and **B = (Bx, By)**, then the resultant vector **C** is: 
C = A - B = (Ax - Bx, Ay - By) 

**For 3D Vectors:** 
If **A = (Ax, Ay, Az)** and **B = (Bx, By, Bz)**, then the resultant vector **C** is: 
C = A - B = (Ax - Bx, Ay - By, Az - Bz) 

Where: 
- **Ax, Ay, Az** are the components of vector A. 
- **Bx, By, Bz** are the components of vector B. 
The mathematical relationship is that vector subtraction is performed by subtracting the corresponding components of the vectors. This operation yields a new vector whose components represent the difference in each dimension, thereby maintaining the directional quality of the original vectors.

## Who should use this

Physicists analyzing force vectors in experiments, software developers working with graphics in game design, and civil engineers calculating displacement vectors in structural analysis. Additionally, navigators using vector subtraction to correct course may find this tool beneficial.

## Worked examples

Example 1: For 2D vectors A = (3, 4) and B = (1, 2), the subtraction is: 
C = A - B = (3 - 1, 4 - 2) = (2, 2). The resulting vector C = (2, 2) indicates a movement from point B to point A in a northeast direction. 

Example 2: For 3D vectors A = (5, 3, 1) and B = (2, 1, 4), the subtraction is: 
C = A - B = (5 - 2, 3 - 1, 1 - 4) = (3, 2, -3). The resulting vector C = (3, 2, -3) shows a change that moves upward and slightly backward in 3D space. These examples illustrate how vector subtraction can represent physical movements in different dimensions.

## Limitations

This tool assumes that all vectors are represented in a Cartesian coordinate system. It cannot handle vectors expressed in polar or spherical coordinates without conversion. Additionally, precision is limited to the floating-point representation of numbers, which can lead to rounding errors in very large or very small values. Edge cases, such as subtracting identical vectors, result in the zero vector, which may not provide useful information in certain applications. Lastly, the calculator does not account for transformations such as rotation or scaling, which may be necessary in specific contexts.

## FAQs

**Q:** How does vector subtraction relate to physical displacement?


**A:** Vector subtraction can represent the change in position or displacement between two points, with the resulting vector indicating the direction and distance from one point to another.


**Q:** Can this tool handle non-Cartesian coordinates for vector input?


**A:** No, this calculator is designed specifically for Cartesian coordinates and does not perform conversions for polar or spherical coordinates.


**Q:** What happens if I subtract a vector from itself?


**A:** The result is the zero vector, which indicates no change in position or direction, effectively representing that the two vectors are identical.


**Q:** How can I interpret the magnitude of the resultant vector?


**A:** The magnitude of the resultant vector can be calculated using the formula √(Cx² + Cy²) for 2D or √(Cx² + Cy² + Cz²) for 3D, providing insight into the distance represented by the vector.

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*Generated from [complete.tools/vector-subtraction-calculator](https://complete.tools/vector-subtraction-calculator)*