Answer
$x=1-2t; y=1; z=\dfrac{1}{2}+2t$
Work Step by Step
The vector equation can be calculated as: $\nabla f(r_0) \cdot (r-r_0)=0$
and $\nabla f \times \nabla g=-2i+2k$
Now, the parametric equations can be written as: $r-r_0+\nabla f(r_0) t$ for $\nabla f( 1,1,\dfrac{1}{2})=\lt 0,-2,2 \gt$:
Thus, $x=1-2t; y=1+0t=1; z=\dfrac{1}{2}+2t$
or, $x=1-2t; y=1; z=\dfrac{1}{2}+2t$
