Answer
a. There is no place where the field is zero, when the currents are in opposite directions.
b. There are places where the field is zero, when the currents are in the same direction.
Work Step by Step
We only need to consider the plane containing both wires, because outside of that plane, there is no chance for the fields to point in opposite directions and cancel because they never point along the same line.
a. Between the wires, their magnetic fields point in the same direction and so they cannot cancel. On either side of the wires, their magnetic fields point in opposite directions but the field due to the nearer wire is always stronger, so they cannot cancel. There is no place where the field is zero when the currents are in opposite directions.
b. Between the wires, their magnetic fields point in opposite directions and they can cancel at points that are equidistant from both wires (i.e., on the line that runs exactly between the 2 parallel wires).
On either side of the wires, their magnetic fields point in the same direction, so they cannot cancel.
