1. Two planes are parallel if their normal vectors are collinear.

With your example because there doesn't exist a such that

2. To get the line of intersection: :

........ ........

Now set a = t. Then you get:

which can be simplified to:

which is the equation of the line of intersection.

3. The next 2 lines should be calculated in just the same way. Have fun!

EDIT: The attached sketch shows thespecialcases: