# How do you use vector components to find the magnitude?

Dec 14, 2014

To find the magnitude of a vector using its components you use Pitagora´s Theorem.

Consider in 2 dimensions a vector $\vec{v}$ given as:
$\vec{v} = 5 \vec{i} + 3 \vec{j}$ (where $\vec{i}$ and $\vec{j}$ are the unit vectors on the x and y axes)

The magnitude of this vector (or its length in geometrical sense) is given using Pitagora's Theorem, as:
$| \vec{v} | = \sqrt{{5}^{2} + {3}^{2}} = 5 , 8$

The same thing applies in 3 dimensions, the only thing is to include the third component.

So if the vector is now given as:
$\vec{v} = 5 \vec{i} + 3 \vec{j} + 2 \vec{k}$
The magnitude will be:
$| \vec{v} | = \sqrt{{5}^{2} + {3}^{2} + {2}^{2}} = 6 , 2$