If A ( 2,2,-3) B ( 5,6,9) ,C (2,7,9) be the vertices of a triangle. The internal bisector of the angle A meets BC at the point D, then find the coordinates of D.

Explanation

Let the coordinates of D are (x,y,z)
`AB= sqrt(9+16+144)=sqrt169=13`
`AC=sqrt(0+25+144)=sqrt169=sqrt13`
`(AB)/(AC)=13/13RightarrowAB=AC`
`(BD)/(DC)=1/1RightarrowBD=DC`
Since, D is divide the line BC in two equal parts parts. So, D is the mid-point of BC.
`x=(5+2)/2=7//2`
`y=(6+7)/2=13//2`
`z=(9+9)/2=9`
So, the coordinates of D are `(7/2,13/2,9)`