find d coordinates of point which trisect d line segment joining the points P(4,2, 6), Q(10, 16,6) plz explain - Maths - Introduction to Three Dimensional Geometry

Question

find d coordinates of point which trisect d line segment joining
the points P(4,2,?6), Q(10,?16,6) plz explain d steps wen we Strt
sq it especially the step in which we get 20! I didnt get it!!

Diksha Verma · Accepted Answer

As shown in figure, since R and S trisect the line segment PQ So, R
divides PQ in 1:2and s divides PQ in 2:1Let, a point divides a line
in m:nAs we know, Formula of coordinates of points=mx2+nx1m+n,
my2+ny1m+n, mz2+nz1m+nWhen m:n=1:2, and (x1,y1,z1)=(4,2,6) and
(x2,y2,z2)=(10,16,6) Coordinates of R, =1×10+2×41+2,
1×16+2×21+2, 1×6+2×61+2 =10+83, 16+43,
6+123 = 183 , 203 , 183 =6,203,6 i e Coordinates of R (6,203,6)
which trisect the line PQ When m:n=2:1, and (x1,y1,z1)=(4,2,6) and
(x2,y2,z2)=(10,16,6) Coordinates of S, =2×10+1×42+1,
2×16+1×22+1, 2×6+1×62+1 =20+43, 32+23,
12+123 = 243 , 343 , 243 =8,343,8 i e Coordinates of S (8,343,8)
which trisect the line PQ

find d coordinates of point which trisect d line segment joining the points P(4,2,?6), Q(10,?16,6). plz explain d steps wen we Strt sq. it especially the step in which we get 20! I didnt get it!!