What is the norm of #< 7 , 5, 1 >#?

1 Answer
David G.
Feb 14, 2016

The 'norm' of a vector is a unit vector in the same direction. To find it we 'normalize' the vector. In this case, the vector is #<7/sqrt75,5/sqrt75,1/sqrt75># or #<7/8.66,5/8.66,1/8.66>#.

Explanation:

To normalize a vector, we divide each of its elements by the length of the vector. To find the length:

#l=sqrt(7^2+5^2+1^2)=sqrt(49+25+1)=sqrt75=8.66#

The norm can be expressed two ways, depending on your preference (and the preferences of the person who will mark your work):

#<7/sqrt75,5/sqrt75,1/sqrt75># or #<7/8.66,5/8.66,1/8.66>#

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