How do you use vector components to find the magnitude?

1 Answer
Gió
Dec 14, 2014

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)
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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#

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