hatj.(2hati-3hatj+2hatk)  এর মান কত?

‍ 🎓 প্রশ্ন: \( \hat{j} \cdot (2\hat{i} - 3\hat{j} + 2\hat{k}) \) এর মান নির্ণয় করো। 💡 সমাধান: আমরা জানি, \(\hat{i} \cdot \hat{i} = 1\) \(\hat{j} \cdot \hat{j} = 1\) \(\hat{k} \cdot \hat{k} = 1\) এবং, \(\hat{i} \cdot \hat{j} = 0\) \(\hat{j} \cdot \hat{k} = 0\) \(\hat{k} \cdot \hat{i} = 0\) তাহলে, \(\hat{j} \cdot (2\hat{i} - 3\hat{j} + 2\hat{k}) = \hat{j} \cdot 2\hat{i} - \hat{j} \cdot 3\hat{j} + \hat{j} \cdot 2\hat{k}\) \( = 2(\hat{j} \cdot \hat{i}) - 3(\hat{j} \cdot \hat{j}) + 2(\hat{j} \cdot \hat{k})\) \( = 2(0) - 3(1) + 2(0)\) \( = 0 - 3 + 0\) \( = -3\) অতএব, \(\hat{j} \cdot (2\hat{i} - 3\hat{j} + 2\hat{k}) = -3 \) 🏆 উত্তর: -3