question_answer

If \[\overrightarrow{a}=3\hat{i}-\hat{j}-4\hat{k},\] \[\overrightarrow{b}=-2\hat{i}+4\hat{j}-3\hat{k}\] and \[\overrightarrow{c}=\hat{i}+2\hat{j}-\hat{k}\] then \[|3\overrightarrow{a}-2\overrightarrow{b}+4\overrightarrow{c}|\] is \[\sqrt{k},\] then k is

Answer:

398