Magnitude of a Vector

The magnitude of a vector is the vector's length. The magnitude of

v

is denoted as

∣ v ∣ .

The magnitude of vertical and horizontal vectors can be read directly from the coordinate system.

When the vector is neither horizontal nor vertical, the Distance Formula can calculate the magnitude.

Substituting the coordinates

(x_{1}, y_{1})

and

(x_{2}, y_{2})

into the Distance Formula, the magnitude can be found.

∣ v ∣ = (x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}

When written in component form, the magnitude can be found by calculating the square root of the sum of the squares of the components.

v = ⟨ a, b ⟩ \Rightarrow ∣ v ∣ = a^{2} + b^{2}

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