Vector Magnitude

Intro

Vector magnitude is calculated by treating the vector as the hypotenuse of a right triangle and using the Pythagorean Theorem on its horizontal ($x$) and vertical ($y$) components ¹.

2D Vectors

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

• Example: For a vector $\mathbf{v}=⟨3,4⟩$, the magnitude is $\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5$.

3D Vectors

$\Vert v\Vert =\sqrt{x^2+y^2+z^2}$

• Example: For a vector $\mathbf{v}=⟨2,3,6⟩$, the magnitude is $\sqrt{2^2+3^2+6^2}=\sqrt{4+9+36}=\sqrt{49}=7$.

Footnotes

1. https://www.wikihow.com/Find-the-Magnitude-of-a-Vector ↩