Final answer:
Parallel vectors have the same direction, and their resultant magnitude is the sum of their magnitudes. Antiparallel vectors have opposite directions, and their resultant magnitude is the absolute value of the difference in their magnitudes. Multiplying a vector by a negative scalar results in an antiparallel vector with the same magnitude.
Step-by-step explanation:
To determine the possible values of vectors that are parallel and antiparallel, one must understand several key concepts about vectors. Magnitudes of vectors are scalar quantities and they always result in positive numbers. When multiplying a vector by a positive scalar, the magnitude changes but the direction remains the same, resulting in a parallel vector.
If a vector is multiplied by a negative scalar, the resulting vector will have the same magnitude but will be antiparallel, meaning it is directed in the opposite direction. For example, if vector Ā has a magnitude of 1.5 units, multiplying it by -2 will result in a vector Ā with a magnitude of 3.0 units, but it will be antiparallel to Ā.
When two vectors are parallel and in the same direction, their resultant vector's magnitude is the sum of their magnitudes. However, if they are antiparallel (parallel but in opposite directions), the resultant vector's magnitude is the absolute value of the difference of their magnitudes. The direction of the resultant in the case of antiparallel vectors will follow the direction of the longer vector. Parallel vectors that are multiplied result in zero, as do antiparallel vectors, but orthogonal vectors (at a 90-degree angle to each other) produce the largest magnitude when multiplied together.