Given a unit vector $v\_1 \in \mathbb{R}^3 : |v\_1| = 1$, let $v\_1 = (x\_1,y\_1,z\_1)$

What's the simplest way to find another unit vector $v\_2 = (x\_2, y\_2, z\_2)$ such that they are perpendicular (ie $v\_1 \cdotp v\_2 = 0$) ?

Notice the constraints are:

\begin{align}
 x\_1x\_2 + y\_1y\_2 + z\_1z\_2 &= 0,\\
 {x\_1}^2 + {y\_1}^2 + {z\_1}^2 &= 1,\\
 {x\_2}^2 + {y\_2}^2 + {z\_2}^2 &= 1.
\end{align}

What is a solution for $x\_2$, $y\_2$, $z\_2$ in terms of $x\_1$, $y\_1$, $z\_1$ that is **easy to express and calculate**?

(Yes there is an infinite family of such vectors $v\_2$ for a given $v\_1$, I just want one, any one)