2D Vector Subtraction Calculator

What is 2D Vector Subtraction?

2D Vector Subtraction is like finding the difference between two movements! Imagine you're a little bird flying in the sky. If you fly in one direction and then want to know how far you are from where you started, 2D Vector Subtraction helps us figure that out. It's like asking, "How do I get back to where I began?"

How to Calculate 2D Vector Subtraction

To subtract two 2D vectors, we follow these friendly steps:

• Start with the first vector (let's call it \(\vec{a}\))
• Flip the direction of the second vector (we'll call this \(-\vec{b}\))
• Add the flipped vector to the first one
• The result is our answer!

Formula

If we have two vectors \(\vec{a} = (a_x, a_y)\) and \(\vec{b} = (b_x, b_y)\), their difference \(\vec{c}\) is:

\[ \vec{c} = \vec{a} - \vec{b} = (a_x - b_x, a_y - b_y) \]

Where:

• \(a_x\) and \(a_y\) are the x and y components of vector \(\vec{a}\)
• \(b_x\) and \(b_y\) are the x and y components of vector \(\vec{b}\)
• \(c_x\) and \(c_y\) are the x and y components of the resulting vector \(\vec{c}\)

Calculation Steps

1. Write down the x and y components of both vectors
2. Subtract the x components: \(c_x = a_x - b_x\)
3. Subtract the y components: \(c_y = a_y - b_y\)
4. The result is a new vector \(\vec{c} = (c_x, c_y)\)

Example

Let's subtract two vectors: \(\vec{a} = (5, 3)\) and \(\vec{b} = (2, 1)\)

1. We have \(\vec{a} = (5, 3)\) and \(\vec{b} = (2, 1)\)
2. Subtract x components: \(5 - 2 = 3\)
3. Subtract y components: \(3 - 1 = 2\)
4. The result is \(\vec{c} = (3, 2)\)

So, \(\vec{a} - \vec{b} = (3, 2)\)

Visual Representation