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If \(\vec{a}\) and \(\vec{b}\) are unit vectors such that \(\vec{a}\cdot \vec{b}=\cos \theta\) then the value of \(\left|\vec{a}+\vec{b}\right|\) is |
\(2\sin \left(\frac{\theta}{2}\right)\) \(2\sin \theta\) \(2\cos \left(\frac{\theta}{2}\right)\) \(2\cos \theta\) |
\(2\cos \left(\frac{\theta}{2}\right)\) |
| \(\begin{aligned}|\vec{a}+\vec{b}|^{2}&=1+1+2\cos \theta\\ &=2(1+\cos \theta)\\ &=4\cos^{2}\frac{\theta}{2}\\ |\vec{a}+\vec{b}|&=2\cos \left(\frac{\theta}{2}\right)\end{aligned}\) |
