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
Answer & explanation
Correct answer: option 3
\(\begin{aligned}|\vec{a}+\vec{b}|^{2}&=1+1+2\cos \theta\\ &=2(1+\cos \theta)\\ &=4\cos^{2}\frac{\theta}{2}\\ |\vec{a}+\vec{b}|&=2\cos \left(\frac{\theta}{2}\right)\end{aligned}\)