Vector Subtraction Calculator

Visualize and calculate the difference between two vectors in 2D or 3D space. Simply input your vectors and explore the results graphically and numerically.

Vector A (Minuend)

$$ \vec{A} = $$

Vector B (Subtrahend)

$$ \vec{B} = $$

Result

Difference Vector ($$ \vec{A} - \vec{B} $$):

Vector Visualization

Understanding Vector Subtraction

Vector subtraction is the operation of finding the vector difference between two vectors. Geometrically, subtracting vector $$ \vec{B} $$ from vector $$ \vec{A} $$ (i.e., $$ \vec{A} - \vec{B} $$) can be visualized as finding a vector that, when added to $$ \vec{B} $$, results in $$ \vec{A} $$. Alternatively, it's equivalent to adding $$ \vec{A} $$ to the negative of $$ \vec{B} $$ ($$ \vec{A} + (-\vec{B}) $$).

In component form, for vectors $$ \vec{A} = [x_1, y_1, z_1] $$ and $$ \vec{B} = [x_2, y_2, z_2] $$, the subtraction $$ \vec{A} - \vec{B} $$ is calculated as follows:

For 2D vectors: $$ \vec{A} - \vec{B} = [x_1 - x_2, y_1 - y_2] $$
For 3D vectors: $$ \vec{A} - \vec{B} = [x_1 - x_2, y_1 - y_2, z_1 - z_2] $$

This calculator simplifies vector subtraction and provides a visual representation in both 2D and 3D, aiding in understanding vector operations in various fields like geometry, physics, and computer graphics.

Learn more about vector subtraction on resources like Wikipedia and Khan Academy.