Answer: When two vectors have equal magnitudes, the maximum and minimum magnitudes of their sum depend on the angle between them. The sum of two vectors is maximized when they are in the same direction (angle = 0 degrees) and minimized when they are in opposite directions (angle = 180 degrees).
Step-by-step explanation:
Maximum Magnitude:
When the two vectors are in the same direction (angle = 0 degrees), the maximum magnitude of their sum occurs. The magnitude of their sum is equal to the sum of their individual magnitudes.
Minimum Magnitude:
When the two vectors are in opposite directions (angle = 180 degrees), the minimum magnitude of their sum occurs. The magnitude of their sum is equal to the absolute difference between their individual magnitudes.
In mathematical terms, if ∣�∣∣A∣ and ∣�∣∣B∣ are the magnitudes of the two vectors, then:
Maximum Magnitude: ∣�+�∣=∣�∣+∣�∣∣A+B∣=∣A∣+∣B∣
Minimum Magnitude: ∣�+�∣=∣∣�∣−∣�∣∣∣A+B∣=∣∣A∣−∣B∣∣