ic..so thats a line of intersection of 2 planes.so the unit vector which is parallel to that line is $\displaystyle \frac{4}{\sqrt{29}},\frac{-3}{\sqrt{29}},\frac{2}{\sqrt{29}} ?$

...... **Right!**
so to deduce, any line which is parallel to another line will have the same direction vector and a point which lies on it..

...... **Right!**
so the equation of the line of intersection is [a,b,c]+s[4,-3,2]..since we are not given any points which is on that line..

...... **Right!**
pls correct me if im wrong..

**Not necessary! You got it.**