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

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Answer 1 · 2016-02-05T21:58:46

$sqrt126$

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 :

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

$=sqrt126$

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