Final answer:
The provided statements discuss concepts in electromagnetism rather than geometry, and use of the right hand rules indicate interactions between currents in perpendicular wires. They do not offer geometric properties to conclude whether lines are parallel.
Step-by-step explanation:
To determine if lines are parallel, we typically look for equal corresponding angles or equal slopes in the case of graphs. However, none of the statements provided directly give us geometric properties of lines; instead, they seem to relate to physics principles, specifically electromagnetism. For instance, statement 'Figure 22.54 Three parallel coplanar wires with currents in the outer two in opposite directions' describes a setup in electromagnetism but does not directly answer any questions about parallel lines in geometry.
Similarly, the statements about long straight wires running perpendicular to each other without touching refer to the magnetic interactions between currents in each wire. Using the right hand rules, we can determine the direction of the magnetic fields and forces between those wires. The right hand rule helps in predicting the direction of the generated magnetic field around a current-carrying conductor. In the case of perpendicular wires without touching, each wire will indeed exert a magnetic force on the other, but there will be no net torque since they do not intersect and thus have no pivot point for the torque to act around.
The what if-then statements and questions about analogies for parallel resistors relate to different phenomena and concepts.