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If for two vectors hat(A) and hat(B),sum...

If for two vectors `hat(A)` and `hat(B)`,sum `(vec(A)+vec(B))` is perpendicular to the diffrence `(vec(A)-vec(B))`. Find the ratio of their magnitude.

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To solve the problem, we need to find the ratio of the magnitudes of two vectors \(\vec{A}\) and \(\vec{B}\) given that their sum \((\vec{A} + \vec{B})\) is perpendicular to their difference \((\vec{A} - \vec{B})\). ### Step-by-Step Solution: 1. **Understanding Perpendicular Vectors**: If two vectors \(\vec{X}\) and \(\vec{Y}\) are perpendicular, their dot product is zero: \[ \vec{X} \cdot \vec{Y} = 0 ...
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