Given, \(\vec{a}=7 \vec{i}-11 \vec{j}-16 \vec{k}, \vec{b}=8 \vec{i}+3 \vec{j}-5 \vec{k}, \vec{c}=-4 \vec{i}-3 \vec{j}+5 \vec{k}\)
\(\because | 2 \vec{a}-3 \vec{b}+4 \vec{c} |\)
\(=|2(7 \vec{i}-11 \vec{j}-16 \vec{k})=3(8 \vec{i}+3 \vec{j}-5 \vec{k})+4(-4 \vec{i}-3 \vec{j}+5 \vec{k})|\)
\( =|14 \vec{i}-22 \vec{j}-32 \vec{k}-24 \vec{i}-9 \vec{j}+15 \vec{k}-16 \vec{i}-12 \vec{j}+20 \vec{k}|\)
\(=|44 \vec{i}-43 \vec{j}+3 \vec{k} |\)
\(=\sqrt{(44)^{2}+(-43)^{2}+(3)^{2}}\)
\(=\sqrt{1936+1849+9}\)
\(=\sqrt{3794} \)
