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