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  4. If sum of two unit vectors is also an unit vector, then the angle between the two vectors is

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Q. If sum of two unit vectors is also an unit vector, then the angle between the two vectors is

Jharkhand CECEJharkhand CECE 2007

Solution:

Let $\vec{a}$ and $\vec{b}$ be two unit vectors $ \therefore |\vec{a}|=|\vec{b}|=1 $ Now, $|\vec{a}+\vec{b}|^{2}=1$ (given) $ |\vec{a}|^{2}+|\vec{b}|^{2}+2 \vec{a} \cdot \vec{b}=1 $ $ 2 \vec{a} \cdot \vec{b}=1-1-1=-1 $ $ \vec{a} \cdot \vec{b}=\frac{-1}{a^{2}} $ $ \begin{array}{l} \therefore |\vec{a}| \cdot|\vec{b}| \cos \theta=-\frac{1}{2} \\ \Rightarrow \theta=\frac{2 \pi}{3} \end{array} $