Magnitude from Rectangular Components

Magnitude from Rectangular Components

If you know the horizontal and vertical parts, use Pythagoras to find the full vector length.

Magnitude from Rectangular Components

If a vector has perpendicular components `Aₓ` and `Aᵧ`, its magnitude can be calculated using Pythagoras' theorem:

**A = √(Aₓ² + Aᵧ²)**

Example

If:

`Aₓ = 3`

`Aᵧ = 4`

then:

`A = √(3² + 4²)`

`= √25`

**A = 5**

Three Dimensions

For:

**A⃗ = Aₓî + Aᵧĵ + A��k̂**

the magnitude is:

**A = √(Aₓ² + Aᵧ² + A��²)**

Why Pythagoras Works

Rectangular components are mutually perpendicular, so they form a right-angled triangle in two dimensions.

Magnitude from Rectangular Components — Advanced

The magnitude is the Euclidean norm of the vector and is independent of the signs of individual components.