Vector Subtraction Calculator

Subtract vectors step by step

The calculator will find the difference of two vectors, with steps shown. It subtracts vectors of any size.

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If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Introducing the Vector Subtraction Calculator. Effortlessly perform vector subtraction and get the resultant vector in a matter of seconds. Our versatile calculator can handle different vectors.

How to Use the Vector Subtraction Calculator?

  • Input

    Enter the first vector in the first input field and the second vector in the second input field. For example, if you're working with 3D vectors, you can enter something like 1,2,3 for the first vector and 4,5,6 for the second one.

  • Calculation

    After you've entered both vectors, click the button to perform the calculation.

  • Result

    The calculator should provide you with the resulting vector from the subtraction operation. For the example vectors given in step 2, the result would be -3,-3,-3. Make sure this matches what you expect based on your own understanding of vector subtraction.

What Is Vector Subtraction?

Vector subtraction is an important operation in linear algebra and is used to determine the difference between two vectors. When subtracting vectors, each pair of corresponding coordinates of the vectors are individually subtracted, and the results are compiled into a new vector.

Suppose we have two vectors in a 2D space, namely, $$$\mathbf{\vec{u}}=\left\langle u_1,u_2\right\rangle$$$ and $$$\mathbf{\vec{v}}=\left\langle v_1,v_2\right\rangle$$$. Then the formula for subtraction is

$$\mathbf{\vec{u}}-\mathbf{\vec{v}}=\left\langle u_1-v_1,u_2-v_2\right\rangle$$

For a 3D space, the formula extends to

$$\mathbf{\vec{u}}-\mathbf{\vec{v}}=\left\langle u_1-v_1,u_2-v_2,u_3-v_3\right\rangle$$

In this case, $$$u_1$$$, $$$u_2$$$, and $$$u_3$$$ are the coordinates of the vector $$$\mathbf{\vec{u}}$$$, while $$$v_1$$$, $$$v_2$$$, and $$$v_3$$$ are the coordinates of the vector $$$\mathbf{\vec{v}}$$$.

What Is the Rule for Vector Subtraction?

The rule for subtracting vectors follows a straightforward principle. Each corresponding coordinate of the two vectors is subtracted separately to form the resultant vector.

Suppose we have two vectors in $$$n$$$-dimensional space $$$\mathbf{\vec{u}}=\left\langle u_1,u_2,\ldots,u_n\right\rangle$$$ and $$$\mathbf{\vec{v}}=\left\langle v_1,v_2,\ldots,v_n\right\rangle$$$.

The rule for subtracting the vector $$$\mathbf{\vec{v}}$$$ from the vector $$$\mathbf{\vec{u}}$$$ (denoted as A - B) can be formulated as follows:

$$\mathbf{\vec{u}}-\mathbf{\vec{v}}=\left\langle u_1-v_1,u_2-v_2,\ldots,u_n-v_n\right\rangle$$

In other words, the first coordinate of the vector $$$\mathbf{\vec{v}}$$$ is subtracted from the first coordinate of the vector $$$\mathbf{\vec{u}}$$$, the second coordinate of vector $$$\mathbf{\vec{v}}$$$ from the second coordinate of vector $$$\mathbf{\vec{u}}$$$, and so on, until all corresponding coordinates are subtracted. This set of results then forms a new vector, which is the difference of the vectors $$$\mathbf{\vec{u}}$$$ and $$$\mathbf{\vec{v}}$$$.

It's important to remember that vector subtraction is not commutative, meaning $$$\mathbf{\vec{u}}-\mathbf{\vec{v}}$$$ does not equal $$$\mathbf{\vec{v}}-\mathbf{\vec{u}}$$$. The order of subtraction matters in vector operations.

Why Choose Our Vector Subtraction Calculator?

  • Ease of Use

    The calculator is designed with user-friendliness in mind, making it simple to use. Just enter the vector coordinates, click the "Calculate" button, and get the result. No complicated steps, no confusion.

  • Accuracy

    Our calculator ensures that the calculations are accurate, eliminating any chances of human error that might occur in manual calculations.

  • Speed

    Instead of performing complex vector subtraction manually, which can be time-consuming, our calculator delivers results in seconds.

  • Versatility

    Our calculator can handle different vectors.


Can this calculator handle 3D vectors?

Yes, our Vector Subtraction Calculator can handle vectors in both 2D and 3D spaces.

Can I use the Vector Subtraction Calculator for vector addition?

No, there is a separate calculator for this operation.

What does the Vector Subtraction Calculator do?

The Vector Subtraction Calculator allows you to calculate the result of subtracting one vector from another. Simply input two vectors of the same dimension, and the tool will return their difference.

What should I do if I get an error?

First, check that you've entered both vectors correctly and that they have the same dimension. If you're still experiencing problems, please contact our support team with a description of the issue and the vectors you entered.