Single line doesn't define unique plane - because it belongs to infinite number of planes in space. So you have to provide additional info about plane.
If there is no additional information concerning this plane, you might want to choose arbitrary plane which this line belongs to:
Let's (dx, dy, dz) is your directionVector. Find 2 elements with bigger magnitude, exchange them, and negate one of them. Set the third element (with the least magnitude) to zero. This vector is perpendicular to directionVector.
Example:
if (dx <= dy) and (dx <= dz) then PV = (0, -dz, dy)
Then normalize this vector uP = PV / |PV| And your target points
Ta = A +- t * uP (two points)
Tb = B +- t * uP (two points)
Note that line AB and all points A, B, Ta1, Ta2, Tb1, Tb2 lie in the same plane (arbitrarily chosen)