Why is the angle 90° when magnitude of sum equals magnitude of difference?

[H.D. M A K]

When magnitude of addition is equals to the magnitude of difference of two vectors then the angle between them will be 90 degrees... How and Why ? can anyone explain it ??
Any help will be appreciated..
Thanks

 

[mfb]

Did you draw a sketch? Can you express the magnitude of the sum and the difference in terms of their individual magnitudes and the angle?

 

[Quantum Defect]

When magnitude of addition is equals to the magnitude of difference of two vectors then the angle between them will be 90 degrees... How and Why ? can anyone explain it ??
Any help will be appreciated..
Thanks

Think about two vectors: (a1, b1, c1, ...) and (a2, b2, c2, ...)
What are the magnitudes of the sum and difference of these two vectors? Set these two equations equal to each other and simplify.
What is the scalar (dot) product of the two vectors? How is this related to the result from the first part?

 

[Mark44]

@H.D. M A K , I split off your other question, and moved it to https://www.physicsforums.com/threads/when-magnitude-of-addition-is-equals-to.795617/.