যদি  vecA=hati,  vecB=hatj+hatk , vecC=hati+hatj+hatk হয়, তাহলে  vecA.(vecBxxvecC) =?

Explanation:

Another Explanation (5): দেওয়া আছে, \( \vec{A} = \hat{i} \), \( \vec{B} = \hat{j} + \hat{k} \), \( \vec{C} = \hat{i} + \hat{j} + \hat{k} \) আমাদের নির্ণয় করতে হবে, \( \vec{A} \cdot (\vec{B} \times \vec{C}) \) প্রথমে, \( \vec{B} \times \vec{C} \) নির্ণয় করি: \( \vec{B} \times \vec{C} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{vmatrix} \) = \( \hat{i}(1 \cdot 1 - 1 \cdot 1) - \hat{j}(0 \cdot 1 - 1 \cdot 1) + \hat{k}(0 \cdot 1 - 1 \cdot 1) \) = \( \hat{i}(1 - 1) - \hat{j}(0 - 1) + \hat{k}(0 - 1) \) = \( 0\hat{i} + \hat{j} - \hat{k} \) = \( \hat{j} - \hat{k} \) এখন, \( \vec{A} \cdot (\vec{B} \times \vec{C}) \) নির্ণয় করি: \( \vec{A} \cdot (\vec{B} \times \vec{C}) = \hat{i} \cdot (\hat{j} - \hat{k}) \) = \( (1 \cdot 0) + (0 \cdot 1) + (0 \cdot -1) \) = \( 0 + 0 + 0 \) = 0 সুতরাং, \( \vec{A} \cdot (\vec{B} \times \vec{C}) = 0 \) 🥳