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The vector of magnitude $3 \sqrt{6}$ along the internal bisector of the angle between the vectors $4 i - 7 j + 4 k$ and $i + 2 j - 2 k$ is.

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$\pm (7 i - j - 2 k)$

$\pm (7 i + j - 2 k)$

$\pm (7 i + 2 j + 2 k)$

$\pm (7 i - j + 2 k)$

answer is C.

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Detailed Solution

$\pm 3 \sqrt{6} (\frac{\frac{4 i - 7 j + 4 k}{9} + \frac{i + 2 j - 2 k}{3}}{|\frac{7 i - j - 2 k}{9}|}) = \pm 3 \sqrt{6} (\frac{7 i - j - 2 k}{\sqrt{49 + 1 + 4}}) \Rightarrow \pm (7 i - j - 2 k)$

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