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Q.
The sum of two unit vectors is a unit vector. The magnitude of their difference is
Vector Algebra
Solution:
Let $\vec{c}=\vec{a}+\vec{b}$ where $\vec{a}, \vec{b}, \vec{c}$ are all unit vectors
$\therefore \vec{c}^{2}=\vec{a}^{2}+\vec{b}^{2}+2\,\vec{a}\cdot\vec{b}$
or $1=1+1+2\,\vec{a}\,.\,\vec{b}$
$\Rightarrow 2\,\vec{a}\,.\,\vec{b}=-1$
Again $\left|\vec{a}-\vec{b}\right|^{2}=\vec{a}^{2}+\vec{b}^{2}-2\,\vec{a}\,.\,\vec{b}$
$=1+1-\left(-1\right)=3$
$\therefore =\left|\vec{a}-\vec{b}\right|=\sqrt{3}$