31. For two vectors \( \vec{A} \) and \( \vec{B} \), if \( \vec{A} \times \vec{B}=6 \hat{\imath}+2 \hat{j}+5 \hat{k}, \vec{A} \cdot \vec{B}=-13, \vec{A}+\vec{B}=2 \hat{i}+\hat{j}+2 \vec{k} \) then find: \( |\vec{A}|=3 \), the vectors \( \vec{A} \) and \( \vec{B} \) a) The two b) The area of the parallelogram and the triangle having \( \vec{A} \) and \( \vec{B} \) as their edge. c) A third vector having magnitude twice \( \vec{A} \) and direction perpendicular to both vectors.

Part-III: Choose the best answer from given choice (1pt eacil) 11. Let \( \mathrm{B}=\{\emptyset,\{\emptyset,\{\emptyset\}\}\} \). Then the number of proper subset is \( \begin{array}{llll}\text { A. } 8 & \text { B. } 7 & \text { C. } 3 & \text { D. } 4\end{array} \)

Explain the difference between exponential growth and exponential decay.

Part-III: Choose the best answer from given choice (Ipt eacil 11. Let \( B=\{\emptyset,\{\emptyset,\{\emptyset\}\}\} \). Then the number of proper subset is \( \begin{array}{llll}\text { A. } 8 & \text { B. } 7 & \text { C. } 3 & \text { D. } 4\end{array} \)

You've produced an entertaining and educational newsletter on Linkedln for the last year. Each edition earns more engagement and subscribers than the last. While being mindful of your limited budget, what is the most strategic way of repurposing this newsletter for a wider audience? Develop an audio adaptation reading through each edition. Develop a weekly discussion in Discord for each edition. Develop a video adaptation visualizing each edition. Dodcast with a new episode for each edition.

Explain the difference between exponential growth and exponential decay.