Answer
$x=1+t,y=-1+2t,z=1+t$
and
$x-1=\frac{y+1}{2}=z-1$
Work Step by Step
Equation of the line is given by $r=r_0+tv$
$r_0=(1,-1,1)$ and $v= \lt 1,2,1 \gt$
Parametric equations are defined by:
$x=x_0+at$, $y=y_0=bt$ and $z=z_0+ct$
Thus, the parametric equations are:
$x=1+t,y=-1+2t,z=1+t$
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:
$x-1=\frac{y+1}{2}=z-1$
