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If $\vec{a}$ and $\vec{b}$ are two unit vectors inclined at an angle $60^{\circ}$ to each other, then which one of the following is correct?
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Verified Answer
The correct answer is:
$|\vec{a}+\vec{b}|>1$
$\begin{aligned}|\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}| &=\sqrt{|\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}|^{2}} \\ &=\sqrt{|\overrightarrow{\mathbf{a}}|^{2}+|\overrightarrow{\mathbf{b}}|^{2}+2|\overrightarrow{\mathbf{a}}| \cdot|\overrightarrow{\mathbf{b}}| \cos 60^{\circ}} \\ &=\sqrt{1^{2}+1^{2}+2 \cdot 1 \cdot 1 \cdot \frac{1}{2}}=\sqrt{3} \\ \therefore|\overrightarrow{\mathbf{a}}+\overrightarrow{\mathbf{b}}|>1 \end{aligned}$
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