Answer
$x=1+5t,y=2t,z=-3t$
and
$\frac{x-1}{5}=\frac{y}{2}=\frac{-z}{3}$
Work Step by Step
We will find the point of intersection between two planes.
In order to find this, take $z=0$
Parametric equations are defined by:
$x=x_0+at$, $y=y_0=bt$ and $z=z_0+ct$
Thus, the parametric equations are:
$x=1+5t,y=2t,z=-3t$
The symmetric equations are defined by:
$\frac{x-x_0}{a}=\frac{y-y_0}{b}=\frac{z-z_0}{c}$
Hence, the symmetric equations are:
$\frac{x-1}{5}=\frac{y}{2}=\frac{-z}{3}$
