The direction ratios of the line bisecting the angle between the x-axis and the line having direction ratios (3, -1, 5) are
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The vectors representing the directions of the angle bisectors between two vectors $\vec{a}$ and $\vec{b}$ are given by $\hat{a} \pm \hat{b}$, where $\hat{a}$ and $\hat{b}$ are the unit vectors. One gives the internal bisector, the other gives the external bisector.