Mathematics - Vector Question with Solution | TestHub

$\hat{i}\times (\bar{a}\times \hat{i})=(\hat{i}\cdot \hat{i})\bar{a}-(\hat{i}\cdot \bar{a})\hat{i}=\hat{j}+2\hat{k}$ $\begin{array}{rl}& \text{ Similarly, }\hat{j}\times (\bar{a}\times \hat{j})=2\hat{i}+2\hat{k}\\ & \hat{k}\times (\bar{a}\times \hat{k})=2\hat{i}+\hat{j}\\ & \Rightarrow \Vert \hat{j}+2\hat{k}{|}^2+|2\hat{i}+2\hat{k}{|}^2+|2\hat{i}+\hat{j}{|}^2\\ & =5+8+5=18\end{array}$