What is the norm or $< 4 , -4 , 9 >$ ?

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Answer 1 · 2016-07-11T13:17:53

$sqrt(113)$

When norm is thought of as a length or distance, we can define the norm of a vector $vec(u) = (u_1,u_2,...,u_n)$ in n-dimensional space $RR^n$ as

$||vec(u)|| -= sqrt(u_1^2+u_2^2+...+u_n^2)$

In this case, the norm will be given by

$||vec(u)|| = sqrt(4^2+(-4)^2+9^2) = sqrt(113)$

What is the norm or < 4 , -4 , 9 >< 4 , -4 , 9 >?