Vector on bisectrix between other two

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Supose $\overrightarrow a=(2,-3,6)$ and $\overrightarrow b=(-1,2,-2)$ are represented in the same origin. Calculate the coordinates of the vector $\overrightarrow c$ that is on the bisectrix of the angle between $\overrightarrow a$ and $\overrightarrow b$, knowing that $|\overrightarrow c|=3 \sqrt {42}$.