Answer
$x=2+t,y=1-t,z=t$
and
$x-2=\frac{y-1}{-1}=z$
Work Step by Step
The direction vector for a line through the $(2,1,0)$ and is perpendicular to $i+j+k$
Equation of the line is given by $r=r_0+tv$
$r_0=(2,1,0) $ and $v= \lt 1,-1,1 \gt$
Parametric equations are defined by:
$x=x_0+at$, $y=y_0=bt$ and $z=z_0+ct$
Thus, the parametric equations are:
$x=2+t,y=1-t,z=t$
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:
$x-2=\frac{y-1}{-1}=z$
