2D Vector Addition Calculator

What is 2D Vector Addition?

2D Vector Addition is like combining two different movements to find out where you end up! Imagine you're a little ant walking on a piece of paper. If you walk forward and then turn right, 2D Vector Addition helps us figure out exactly where you'll be at the end of your journey.

How to Calculate 2D Vector Addition

To add two 2D vectors, we follow these simple steps:

• Line up the tails of the vectors
• Add the x-components of both vectors
• Add the y-components of both vectors
• Draw a new vector from the tail to the tip of the combined movements

Formula

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

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

Calculation Steps

1. Write down the x and y components of both vectors
2. Add the x components: \(c_x = a_x + b_x\)
3. Add 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 add two vectors: \(\vec{a} = (3, 2)\) and \(\vec{b} = (1, 4)\)

1. We have \(\vec{a} = (3, 2)\) and \(\vec{b} = (1, 4)\)
2. Add x components: \(3 + 1 = 4\)
3. Add y components: \(2 + 4 = 6\)
4. The result is \(\vec{c} = (4, 6)\)

So, \(\vec{a} + \vec{b} = (4, 6)\)

Visual Representation