How do you use vector components to find the magnitude?

Question

How do you use vector components to find the magnitude?

1 Answer

Impact of this question

16780 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-12-14T15:43:43

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

Consider in 2 dimensions a vector $\to v$ $vecv$ given as:
$\to v = 5 \to i + 3 \to j$ $vecv = 5veci + 3vecj$ (where $\to i$ $veci$ and $\to j$ $vecj$ are the unit vectors on the x and y axes)
enter image source here
The magnitude of this vector (or its length in geometrical sense) is given using Pitagora's Theorem, as:
$∣ ∣ \to v ∣ ∣ = \sqrt{5^{2} + 3^{2}} = 5, 8$ $|vecv| =sqrt(5^2+3^2)= 5,8$

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

So if the vector is now given as:
$\to v = 5 \to i + 3 \to j + 2 \to k$ $vecv = 5veci+ 3vecj + 2veck$
The magnitude will be:
$∣ ∣ \to v ∣ ∣ = \sqrt{5^{2} + 3^{2} + 2^{2}} = 6, 2$ $|vecv|= sqrt(5^2+3^2+2^2) = 6,2$

Science

Math

Humanities

... and beyond

How do you use vector components to find the magnitude?

1 Answer

Related questions

Impact of this question