Squeeze theorem of multivariable functions

My Question is the following: Let F: U $ \subset \mathbb{R}^n$ $ \rightarrow \mathbb{R}^m$ where U is an open set containing a punctured neighbourhood of a. Let G : $ U \subset \mathbb{R}^n \rightarrow \mathbb{R}^{\geq 0}$ . Assume $ 0 \leq |f(x)| \leq h(x)$ ( Note, here |.| denotes the magnitude of the vector. Show that if limit of h(x) as x approaches a is 0 then the limit of f(x) as x approaches a is 0. Note that I get the general idea; however, what i’m stuck on is showing that
|f(x)|$ \leq$ h(x)$ \leq$ $ |h(x)|$ . I’m not sure why that follows and what it means because h(x) is a vector, and the absolute value is the length of the vector..