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

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For two vectors A and B with equal magnitudes, the angle between them affects the magnitudes of A + B and A - B. The magnitude of A + B can be expressed using the cosine of the angle between the vectors, while A - B will also depend on this angle. If A and B point in the same direction, A - B equals zero, which is not the case here. To find the angle that makes the magnitude of A + B larger than A - B by a factor of n, vector addition rules must be applied. Understanding these relationships is crucial for solving the problem correctly.
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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 \vec A and \vec B have the same magnitude, but \vec A-\vec B does not equal zero unless they point in the same direction. You have to use the rules of vector addition to write out what \vec A+\vec B and \vec A-\vec B are.
 

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