Question

How do you use vector components to find the magnitude?

Answer 1

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

Consider in 2 dimensions a vector `vecv` given as:
`vecv = 5veci + 3vecj` (where `veci` and `vecj` 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:
`|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:
`vecv = 5veci+ 3vecj + 2veck`
The magnitude will be:
`|vecv|= sqrt(5^2+3^2+2^2) = 6,2`