Let \(\left\{\mathbf{X}_{n}ight\}_{n=1}^{\infty}\) be a sequence of \(d\)-dimensional random vectors that converge in distribution to a random vector \(\mathbf{X}\) as \(n ightarrow \infty\). Let \(\mathbf{X}_{n}^{\prime}=\left(X_{n 1}, \ldots, X_{n d}ight)\) and \(\mathbf{X}^{\prime}=\left(X_{1}, \ldots, X_{d}ight)\). Prove that if \(\mathbf{X}_{n} \xrightarrow{d} \mathbf{X}\) as \(n ightarrow \infty\) then \(X_{n k} \xrightarrow{d} X_{k}\) as \(n ightarrow \infty\) for all \(k \in\{1, \ldots, d\}\).