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If  \(\vec a=3\hat i-\hat j-4\hat k,\)  \(\vec b= 2\hat i+4\hat j-3\hat k\)  and  \(\vec a=\hat i+2\hat j-\hat k,\)  find  |\(3\vec a-2\vec b+4\vec c\)|.

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The magnitude of any vector  \(\vec a=a_1\hat i+a_2\hat j+a_3\hat k\) can be written as

\(\sqrt{291}\)

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