Given: The vertices of the triangle are A(1, 2, 3), B(0, 4, 1) and C(-1, -1, -3)

To find: the coordinates of D

Formula used:

Distance Formula:

The distance between any two points (a, b, c) and (m, n, o) is given by,

Section Formula:

A line AB is divided by C in m:n where A(x, y, z) and B(a, b, c).

The coordinates of C is given by,

We know angle bisector divides opposite side in the ratio of the other two sides.

As AD is angle bisector of A and meets BC at D

⇒ BD : DC = AB : BC

Distance between A(1, 2, 3) and B(0, 4, 1) is AB,

= 3

Distance between A(1, 2, 3) and C(-1, -1, -3) is AC,

= 7

AB : AC = 3:7

⇒ BD: DC = 3:7

Therefore, m = 3 and n = 7

B(0, 4, 1) and C(-1, -1, -3)

Coordinates of D using section formula:

Hence, Coordinates of D are