2D Vector Magnitude Calculator

What is 2D Vector Magnitude?

Imagine you're a superhero who can fly! The 2D Vector Magnitude is like measuring how far you've flown in a straight line, even if you've zigzagged a bit. It's the length of an arrow that points from where you started to where you ended up.

How to Calculate 2D Vector Magnitude

To find the magnitude of a 2D vector, we use the Pythagorean theorem. It's like measuring the longest side of a right triangle! Here's how we do it:

• Square the x-component of the vector
• Square the y-component of the vector
• Add these squared values
• Take the square root of the sum

Formula

For a vector \(\vec{v} = (x, y)\), its magnitude \(|\vec{v}|\) is:

\[ |\vec{v}| = \sqrt{x^2 + y^2} \]

Calculation Steps

1. Write down the x and y components of your vector
2. Square the x-component: \(x^2\)
3. Square the y-component: \(y^2\)
4. Add the squared values: \(x^2 + y^2\)
5. Take the square root of the sum: \(\sqrt{x^2 + y^2}\)

Example

Let's find the magnitude of the vector \(\vec{v} = (3, 4)\)

1. We have \(\vec{v} = (3, 4)\)
2. Square x: \(3^2 = 9\)
3. Square y: \(4^2 = 16\)
4. Add squared values: \(9 + 16 = 25\)
5. Take the square root: \(\sqrt{25} = 5\)

So, the magnitude of \(\vec{v}\) is 5 units.

Visual Representation