Let `A(3,2,0),\ B(5, 3,2),\ C(-9,6,-3)` be three points forming a triangle. The bisector `A D\ of\ /_B A C` meets sides in D. Find the coordinates of D.

Explanation

Given that `A(3,2,0),\ B(5,3 ,2),\ C(-9,6,-3)`
be three points forming a triangle.
The bisector `A D\ of\ /_B A C`
meets sides in D.
we have to find the coordinate of `D`
so `AB=sqrt((3-5)^2+(2-3)^2+(0-2)^2`
`=sqrt(4+1+4)`
`=9`
`AC=sqrt((3+9)^2+(2-6)^2+(0+3)^2`
`=sqrt(144+16+9)`
`=13`
as The bisector `A D\ of\ /_B A C`
meets sides in D
so,`BD:DC=AB:AC=3:13`
By using Section formula,
`D=((3(-9)+13(5))/(3+13),(3(6)+13(3))/(3+13),(3(-3)+13(2))/(3+13))`
`=(-38/16,57/16,17/16)`
`=(-19/8,57/16,17/16)`