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In the triangle with vertices $\mathrm{A}(3,2,0), \mathrm{B}(5,3,2)$ and $\mathrm{C}(-9,6,-3)$, the bisector of $\lfloor B A C$ meets $\mathrm{BC}$ at $\mathrm{D}$. The coordinates of $\mathrm{D}$ are

MathematicsThree Dimensional GeometryAP EAMCETAP EAMCET 2017 (24 Apr Shift 1)

Options:

A $\left(\frac{57}{16}, \frac{38}{16}, \frac{17}{16}\right)$
B $\left(\frac{38}{16}, \frac{57}{16}, \frac{17}{16}\right)$
C $\left(\frac{38}{16}, \frac{17}{16}, \frac{57}{16}\right)$
D $\left(\frac{17}{16}, \frac{38}{16}, \frac{57}{16}\right)$

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