Answer
$r=\lt u, v, \dfrac{16-2u+4 v}{3} \gt$; $ u, v \in (-\infty, + \infty)$
Work Step by Step
Let us consider that $r=\lt u, v \gt$ defines the parametric description of the plane.
We are given the equation of a plane as: $2x -4y+3z=16 \implies z=\dfrac{16-2x+4y}{3} ~~~~(1)$
Here, $u=x $ and $v=y$, so we can write the equation (1) as:
$z=\dfrac{16-2u+4 v}{3}$ and $ u, v \in (-\infty, + \infty)$
Thus, the parametric description of the plane can be expressed as:
$r=\lt u, v, \dfrac{16-2u+4 v}{3} \gt$; $ u, v \in (-\infty, + \infty)$
