Question

Find $2\overline{j}\times \left(3\overline{i}-4\overline{k}\right)\left(\overline{i}-2\overline{j}\right)\times \overline{k}.$

Answer 1

$[2\hat{j}\times (3\hat{i}-4\hat{k}\left)\right]\left[\right(\hat{i}-2\hat{j})\times \hat{k}]$

$\Rightarrow \left[6\right(\hat{j}\times \hat{i})-8(\hat{j}\times \hat{k}\left)\right][\hat{i}\times \hat{k}-2\hat{j}\times \hat{k}]$

$\Rightarrow \left[6\right(-\hat{k})-8(\hat{i}\left)\right]\left[\right(-\hat{j})-2(\hat{i}\left]\right)$

$\Rightarrow (-6\hat{k}-8\hat{i})(-\hat{j}-2\hat{i})$

$\Rightarrow 2(3\hat{k}+4\hat{i})(\hat{j}+2\hat{i})$

$\Rightarrow 2[3\hat{k}.\hat{j}+6\hat{k}.\hat{i}+4\hat{i}.\hat{j}+8|\hat{i}{|}^2]$

$\Rightarrow 2\left[3\right(0)+6(0)+4(0)+8]$

$\Rightarrow 16$

$\therefore [2\hat{j}\times (3\hat{i}-4\hat{k}\left)\right(\hat{i}-2\hat{j})\times \hat{k}]=16$