এদের মধ্যবর্তী কোণ-

ধরি, \( \vec{a} = \hat{i} - \hat{j} \) এবং \( \vec{b} = \hat{j} - \hat{k} \)।

\( \vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos{\theta} \)

এখানে, \( \vec{a} \cdot \vec{b} = (1)(0) + (-1)(1) + (0)(-1) = -1 \)

\(|\vec{a}| = \sqrt{1^2 + (-1)^2 + 0^2} = \sqrt{2}\)

\(|\vec{b}| = \sqrt{0^2 + 1^2 + (-1)^2} = \sqrt{2}\)

সুতরাং, \( \cos{\theta} = \frac{\vec{a} \cdot \vec{b}}{|\vec{a}| |\vec{b}|} = \frac{-1}{\sqrt{2} \cdot \sqrt{2}} = \frac{-1}{2} \)

\( \theta = \cos^{-1}\left(-\frac{1}{2}\right) = 120^\circ \) 😮

অতএব, এদের মধ্যবর্তী কোণ 120°। 🎉