Complete the parametric equations for the line where the planes $6 x-12 y+2 z=8$ and $7 x-15 y-3 z=21$ intersect.
$x(t)=66 t$
$y(t)=$
\[
z(t)=
\]

Step 1 ：We are given two planes $6 x-12 y+2 z=8$ and $7 x-15 y-3 z=21$. The intersection of these two planes forms a line. We need to find the parametric equations of this line.

Step 2 ：We start by rearranging the equations of the planes to isolate x, y, and z. The rearranged equations are $x = 2y - \frac{z}{3} + \frac{4}{3}$ and $x = \frac{15y}{7} + \frac{3z}{7} + 3$.

Step 3 ：We set x equal to a parameter t, and solve for y and z in terms of t. The substituted equations are $t = 2y - \frac{z}{3} + \frac{4}{3}$ and $t = \frac{15y}{7} + \frac{3z}{7} + 3$.

Step 4 ：Solving these equations, we get $y = \frac{16t}{33} - 1$ and $z = -\frac{t}{11} - 2$.

Step 5 ：\(\boxed{x(t)=66 t}\)

Step 6 ：\(\boxed{y(t)=\frac{16t}{33} - 1}\)

Step 7 ：\(\boxed{z(t)=-\frac{t}{11} - 2}\)