Final answer:
The question asks for the value of y that makes lines a and b parallel, but insufficient information is provided to determine this directly. Typically, lines are parallel if they have equal slopes or their angles correspond, but the additional context given does not relate to the question.
Step-by-step explanation:
To find the value of y for which line a is parallel to line b, we need to know more context that is not provided in the question. Usually, to determine if two lines are parallel, their slopes must be equal in a Cartesian plane (y = mx + b) or their angles must correspond in some way when given geometric figures. Since the question seems to refer to angles, we would look for situations where corresponding angles are equal or alternate interior angles are equal, etc.
However, the additional information provided is unrelated to the question, discussing vectors and unrelated mathematical solutions instead of giving information about lines a and b.