vecA + vecB = 12hati - 4hatj + 8hatk, vecA - vecB = -6hati + 12hatj + 10hatk

 vecA . vecB  এর মান কত?

\( \vec{A} + \vec{B} = 12\hat{i} - 4\hat{j} + 8\hat{k} \) .....(1)

\( \vec{A} - \vec{B} = -6\hat{i} + 12\hat{j} + 10\hat{k} \) .....(2)

\( 2\vec{A} = (12-6)\hat{i} + (-4+12)\hat{j} + (8+10)\hat{k} \)

\( 2\vec{A} = 6\hat{i} + 8\hat{j} + 18\hat{k} \)

\( \vec{A} = 3\hat{i} + 4\hat{j} + 9\hat{k} \)

\( 2\vec{B} = (12+6)\hat{i} + (-4-12)\hat{j} + (8-10)\hat{k} \)

\( 2\vec{B} = 18\hat{i} - 16\hat{j} - 2\hat{k} \)

\( \vec{B} = 9\hat{i} - 8\hat{j} - \hat{k} \)

\( \vec{A} \cdot \vec{B} = (3\hat{i} + 4\hat{j} + 9\hat{k}) \cdot (9\hat{i} - 8\hat{j} - \hat{k}) \)

\( \vec{A} \cdot \vec{B} = (3 \times 9) + (4 \times -8) + (9 \times -1) \)

\( \vec{A} \cdot \vec{B} = 27 - 32 - 9 \)

\( \vec{A} \cdot \vec{B} = -14 \)