Angle for A + B = n times A - B Magnitude

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SUMMARY

The discussion centers on determining the angle between two vectors A and B of equal magnitudes, such that the magnitude of A + B exceeds that of A - B by a factor of n. It is established that A - B equals zero only when the vectors are aligned in the same direction, which is not the case here. The correct approach involves applying vector addition rules to derive the magnitudes of A + B and A - B, leading to a specific angle calculation based on the given factor n.

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Homework Statement



two vectors A and B have precisely equal magnitudes. For the magnitude of A +B to be larger than the magnitude of A-B by the factor n, what must be the angle between them?

Homework Equations


The Attempt at a Solution



i don't understand this because a-b would equal 0. so wouldn't the angle just be 0 degrees?
 
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Hi BeckyStar678,

BeckyStar678 said:

Homework Statement



two vectors A and B have precisely equal magnitudes. For the magnitude of A +B to be larger than the magnitude of A-B by the factor n, what must be the angle between them?


Homework Equations





The Attempt at a Solution



i don't understand this because a-b would equal 0. so wouldn't the angle just be 0 degrees?

The vectors [itex]\vec A[/itex] and [itex]\vec B[/itex] have the same magnitude, but [itex]\vec A-\vec B[/itex] does not equal zero unless they point in the same direction. You have to use the rules of vector addition to write out what [itex]\vec A+\vec B[/itex] and [itex]\vec A-\vec B[/itex] are.
 

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