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Q.
If $\vec{a}$ and $\vec{b}$ are two unit vectors inclined to $x$-axis at angles $30^°$ and $120^°$ respectively, then $\left|\vec{a}+\vec{b}\right|$ equals
Vector Algebra
Solution:
Clearly, angle between $\vec{a}$ and $\vec{b}=\frac{\pi}{2}$
$\Rightarrow \vec{a}\cdot\vec{b}=0$
$\therefore \left|\vec{a}+\vec{b}\right|^{2}=\left|\vec{a}\right|^{2}+\left|{\vec{b}}\right|^{2}+2\vec{a}\cdot\vec{b}$
$=1+1+0=2$
$\Rightarrow \left|\vec{a}+\vec{b}\right|=\sqrt{2}$