Question: Equation of a line

Problem: Write the equation of the straight line (d) through the point A(1,-2,3), cut the straight line 

Delta: x = 3*t+1, y = t, z = t-1 and parallel to the plane (P): x + 2*y + 3*z + 4 = 0.

We know that, if the straight line (d) through the point A and parallel to the plane (P), then (d) lies on a plane (Q), which (Q) through the point A and parallel to the plane (P).

first step: Write the  equation of the plane (Q) through the point A and parallel to the plane (P).

second step: Find the point of intersection B of Delta and (Q).

Third step: (d)  passing through two points A and B.

This is my code. 

with(geom3d);

point(A,1,-2,3);

line(Delta,[3*t+1,t,t-1],t);

plane(P,x + 2*y + 3*z + 4 = 0,[x,y,z]);

n:=NormalVector(P);

plane(Q,[A,n],[x,y,z]);

Equation(Q);

intersection(B,Delta,Q);

Equation(line(AB,[A,B],t));

Please comment about my code. Thank you very much.