Vector Magnitude in a Plane

What is a Vector?

A vector in a plane is a quantity that has both magnitude (size) and direction. It is often represented as an arrow where the length indicates the magnitude and the arrowhead shows the direction.

Understanding Vector Magnitude

The magnitude of a vector is its length. For a vector $\mathbf{v} = (x, y)$ in the Cartesian plane, the magnitude is calculated using the Pythagorean theorem:

$$|\mathbf{v}| = \sqrt{x^2 + y^2}$$

Steps to Calculate Vector Magnitude

1. Identify the components: Find the $x$ and $y$ components of the vector.
2. Square each component: Calculate $x^2$ and $y^2$.
3. Add the squares: Sum the squared components.
4. Find the square root: Take the square root of the sum to find the magnitude.

Examples

Example 1: Calculate the Magnitude of a Vector

Example 2: Calculate the Magnitude of a Vector