# Vector Problem

## Homework Statement

Prove that Vector A is perpendicular to Vector B if |VectorA + VectorB| = |VectorA-VectorB| and use this to prove that the angle formed by joining any point on a circle to the end points of a diameter is 90 degrees,

## The Attempt at a Solution

I really have no idea where to begin, i no that VectorA (dot) VectorB=0 for them to be perpendicular but i still dont really understand the second part of the problem, if somebody could point me in the right direction that would be appreciated thank you

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Dick
Homework Helper
(A+B).(A+B)=A.A+2A.B+B.B. What's (A-B).(A-B)? How can they be equal? For the circle problem take A to be the vector connecting the center of the circle to your point and B to be the vector connecting the center to one of the endpoints of the diameter. Do you see it now?

For the first part i meant that if |A+B|=|A-B| then A and B are perpendicular and i forgot to note it is in 3 space A(Ai,Aj,Ak), and i see what your saying for the second part but as i am picturing it the angle will be any angle depending on the vectors? Like if the vectors are perpendicular of coarse the angle will be 90degrees but the way i am understanding the question is that no matter what the angle will be 90 degrees

Dick