If a → = 2 i ^ + j ^ - 3 k ^ ,   b → = i ^ - 2 j ^ + k ^ ,   c → = - i ^ + j ^ -…

Given

$\overrightarrow{a}=2\hat{i}+\hat{j}-3\hat{k}$

$\overrightarrow{b}=\hat{i}-2\hat{j}+\hat{k}$

$\overrightarrow{c}=-\hat{i}+\hat{j}-4\hat{k}$

$\overline{d}=\hat{i}+\hat{j}+\hat{k}$

Now,

$\overrightarrow{a}\times \overrightarrow{b}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 1& -3\\ 1& -2& 1\end{array}\right|$

          $=-5\hat{i}-5\hat{j}-5\hat{k}$

$\overrightarrow{c}\times \overrightarrow{d}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ -1& 1& -4\\ 1& 1& 1\end{array}\right|$

           $=5\hat{i}+3\hat{j}-2\hat{k}$

Now,

$\left(\overrightarrow{a}\times \overrightarrow{b}\right)\times \left(\overrightarrow{c}\times \overrightarrow{d}\right)=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ -5& -5& -5\\ 5& 3& -2\end{array}\right|$

                              $=25\hat{i}-35\hat{j}+10\hat{k}$

$\left|\left(\overrightarrow{a}\times \overrightarrow{b}\right)\times \left(\overrightarrow{c}\times \overrightarrow{d}\right)\right|=\sqrt{625+1225+100}=\sqrt{1950}=5\sqrt{78}$