Question

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

Answer 1

`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`