What is #|| <1, 9, 7 > - < 2, -1, 2> ||#?

1 Answer
Trevor Ryan.
Feb 5, 2016

#sqrt126#

Explanation:

When adding or subtracting vectors in #RR^n# we may simply add or subtract every component individually.

#therefore(1,9,7)-(2,-1,2)=(1-2,9-(-1),7-2))#

#=(-1,10,5)#.

Now the norm of a vector in #RR^n# may be found using the generalized Pythagoras Theorem, so in this case :

#||(-1,10,5)||=sqrt((-1)^2+10^2+5^2)#

#=sqrt126#

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