Chapter 11 - Section 11.5 - Lines and Planes in Space - Exercises - Page 631: 58

$x=1+14t; y=2t; z=15t$

Let us take $y=0$ We have the equation of a plane: $3x-2z=3$ and $2x-2z=2$ $\implies x=1$ and $z=x-1=1-1=0$ Thus, $r_0=\lt 1,0,0 \gt$ We know that $r=r_0+tv$ and $v=\lt 14,2,15 \gt$ Thus, our parametric equation become: $x=1+(14)t; y=0+2t; z=0+15t=15t$ Hence, our parametric equations are: $x=1+14t; y=2t; z=15t$