From given, G1 is the centroid of triangle BCD, G1=(
13
3
,
6
3
,
9
3
) G2 is the centroid of triangle CDA, G2=(
12
3
,
7
3
,
7
3
) As the lines AG1,BG2,CG3,DG4 are concurrent, so point of concurrence of these four lines is point of intersection of lines AG1 and BG2 . The equation of line AG1 is,
x−3
4∕3
=
y−2
0
=
z+1
12
3
=r1 So, the point on line AG1 is (3+
4
3
r1,2,−1+
12
3
r1) and line BG2 is
x−4
0
=
y−1
4
5
=
z−1
4
3
=r2 So, the point on line BG2 is (4,1+
4
3
r2,1+
4
3
r2) Let above point to be point of intersection, 3+
4
3
r1=4⇒2=1+
4
3
r2 And −1+
12
3
r1=1+
4
3
r2 From above values, r1=
3
4
,r2=
3
4
So, the required point of concurrence is (4, 2, 2) .