The vertices of a triangle are A(1,0,2),B(2,3,0),C(0,0,4) then the symmetric form of the line passing through centroid of the triangle and one vertex B is

The centroid of the triangle formed by the points A(1,0,2),B(2,3,0),C(0,0,4)  is G=1+23,33,2+43=(1,1,2)The equation of the line joining two points A(x1,y1,z1) and B(x2,y2,z2) is x−x1x2−x1=y−y1y2−y1=z−z1z2−y1The equation of the line joining two points (1,1,2) and 2,3,0 is x−12−1=y−13−1=z−20−2This can be rewrite as x−11=y−12=z−2−2