Find the coordinates of the points which trisect the line segment joining the points P(4,2, - 6) and Q(10, - 16,6).

Let the point R1, trisects the line PQ i.e., it divides the line in the ratio 1:2⇒R1=1×10+2×41+2,1×(−16)+2×21+2,1×6+2×(−6)1+2=10+83,−16+43,6−123=183,−123,−63=(6,−4,−2)Again, let the point R2 divides PQ internally in the ratio 2: 1. Then, ⇒ R2=2×10+1×42+1,2×(−16)+1×22+1,2×6+1×(−6)1+2=20+43,−32+23,12−63=243,−303,63=(8,−10,2)Hence, required points are (6,-4, - 2) and (8, - 10,2).