How do I construct two vectors $a,b\in \mathbb{R}^{n}$, $a=(a_1,a_2,\ldots a_n)^{T}$ and $b=(b_1,b_2,\ldots b_n)^{T}$ which satisfy in the following conditions ‎\begin{align} & a_ib_i\geq 1,a_ib_j<1, i\neq j, \quad i,j=1,2,\ldots n,\\ & \hspace{40 mm} or\\ & a_ib_i> 1,a_ib_j\leq1, i\neq j, \quad i,j=1,2,\ldots n. ‎\end{align}

How do I construct two vectors $a,b\in \mathbb{R}^{n}$, $a=(a_1,a_2,\ldots, a_n)^T$ and $b=(b_1,b_2,\ldots, b_n)^T$ which satisfy in the following conditions ‎\begin{align} & a_ib_i\geq 1,a_ib_j<1, i\neq j, \quad i,j=1,2,\ldots, n,\\ & \hspace{40 mm} \text{or}\\ & a_ib_i> 1,a_ib_j\leq1, i\neq j, \quad i,j=1,2,\ldots, n. ‎\end{align}

How do I construct two vectors $a,b\in \mathbb{R}^{n}$, $a=(a_1,a_2,\ldots a_n)^{T}$ and $b=(b_1,b_2,\ldots b_n)^{T}$ which satisfy in the following conditions ‎\begin{align} & a_ib_i\geq 1,a_ib_j<1, i\neq j, \quad i,j=1,2,\ldots n,\\ & or\\ & a_ib_i> 1,a_ib_j\leq1, i\neq j, \quad i,j=1,2,\ldots n. ‎\end{align}

How do I construct two vectors $a,b\in \mathbb{R}^{n}$, $a=(a_1,a_2,\ldots a_n)^{T}$ and $b=(b_1,b_2,\ldots b_n)^{T}$ which satisfy in the following conditions ‎\begin{align} & a_ib_i\geq 1,a_ib_j<1, i\neq j, \quad i,j=1,2,\ldots n,\\ & \hspace{40 mm} or\\ & a_ib_i> 1,a_ib_j\leq1, i\neq j, \quad i,j=1,2,\ldots n. ‎\end{align}