A random vector is a random variables whose values are vectors.
Let $x: \Omega \to \R ^n$ be a random vector, so that \[ x(\omega ) = \bmat{x_1(\omega ) \\ x_2(\omega ) \\ \cdots \\ x_3(\omega )}. \]
\[ x(\omega ) = \bmat{x_1(\omega ) \\ x_2(\omega ) \\ \cdots \\ x_3(\omega )}. \]