Aspire Faculty ID #18322 · Topic: AMU MCA 2017 · Just now
AMU MCA 2017

If the sum of two unit vectors is again a unit vector, then magnitude of their difference is

Solution

$ |\vec a+\vec b|=1,\ |\vec a|=|\vec b|=1 $ $ |\vec a+\vec b|^2=|\vec a|^2+|\vec b|^2+2\vec a\cdot\vec b $ $ 1=1+1+2\vec a\cdot\vec b $ $ \Rightarrow \vec a\cdot\vec b=-\frac{1}{2} $ Now, $ |\vec a-\vec b|^2=1+1-2\left(-\frac{1}{2}\right)=3 $ $ \Rightarrow |\vec a-\vec b|=\sqrt{3} $
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