CUET Preparation Today
If \(x\) and \(y\) are unit vectors and \(\phi\) is the angle between them, then \(\frac{1}{2}\left|x-y\right|\) is equal to |
\(0\) \(\frac{\pi}{2}\) \(\sin \left(\frac{\phi}{2}\right)\) \(\cos \left(\frac{\phi}{2}\right)\) |
\(\sin \left(\frac{\phi}{2}\right)\) |
| \(\begin{aligned}|x-y|^{2}&=1+1+2\cos \phi\\ &=4\sin^{2}\frac{\phi}{2}\\ |x-y|&=2\sin \frac{\phi}{2}\\ \sin\left(\frac{\phi}{2}\right)&=\frac{1}{2}|x-y|\end{aligned}\) |
