Final answer:
To rank groups of vectors by resultant magnitude, understand that the largest resultant occurs when all vectors align in the same direction, and the smallest when they cancel each other out. The specific order depends on the internal arrangement within each group.
Step-by-step explanation:
When ranking the groups of vectors from greatest resultant magnitude to smallest resultant magnitude, consider the direction of each vector and how they combine. The largest resultant force vector occurs when all vectors point in the same direction, adding up to 4f, where 'f' is the magnitude of one vector. The smallest resultant is when vectors cancel each other out, such as two pairs pointing in opposite directions, resulting in zero magnitude. So, the ranking depends on the relative directions of vectors within each group.
For example, if Group Q vectors are all pointing in the same direction, their resultant magnitude would be the largest. If Group S vectors cancel each other out in pairs, then its resultant magnitude would be the smallest. Without specific directions, it's not possible to rank the groups. To find the resultant vector, place vectors head to tail geometrically or use analytical methods to add their components.
When two vectors A and B are added, the greatest resultant occurs when they are in the same direction, and the magnitude is simply A+B. Conversely, the smallest resultant magnitude is when they oppose each other, resulting in A-B, which can be zero if A and B are equal in magnitude.