Difference between the norm and absolute value of a given vector.

Question

Let's say I'm given a vector $x=(2, 3, 4)$, and the directions say to find the norm and absolute value of the vector. From what I've found, it's $\sqrt {(2^2 + 3^2 + 4^2)}$ for the absolute value. How about the norm, or are they the same?

Answer 1

Usually "absolute value" applies to a number, not a vector, although the notation $|{\bf a}|$ is sometimes used instead of $\|{\bf a}\|$ for the Euclidean norm.