Question:
The angle between the vectors \(\hat{i} – \hat{j}\) and \(\hat{j} – \hat{k}\) is
सदिशों \(\hat{i} – \hat{j}\) और \(\hat{j} – \hat{k}\) के बीच का कोण क्या है?
Options:
- 0
- \(\dfrac{\pi}{3}\)
- \(\dfrac{2\pi}{3}\)
- \(-\dfrac{\pi}{3}\)
- 0
- \(\dfrac{\pi}{3}\)
- \(\dfrac{2\pi}{3}\)
- \(-\dfrac{\pi}{3}\)
Correct Answer: c)
Explanation:
\(\cos\theta = \dfrac{(\hat{i}-\hat{j}) \cdot (\hat{j}-\hat{k})}{|\hat{i}-\hat{j}| |\hat{j}-\hat{k}|} = \dfrac{-1}{\sqrt{2} \cdot \sqrt{2}} = -\dfrac{1}{2} \implies \theta = \dfrac{2\pi}{3}\).
\(\cos\theta = \dfrac{-1}{\sqrt{2} \times \sqrt{2}} = -\dfrac{1}{2} \implies \theta = \dfrac{2\pi}{3}\)।