Answer :

Given: Points P(4, 2, -6) and Q(10, -16, 6)


To find: the coordinates of points which trisect the line PQ


Formula used:


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,



Let Point R(x, y, z) and Point S(a, b, c) trisects line PQ


So, PR : RS : SQ = 1 : 1 : 1



Now, we will firstly apply section formula on PQ and find coordinates of R


Therefore, m = 1 and n = 2


P(4, 2, -6) and Q(10, -16, 6)


Coordinates of R using section formula:






Now, we will apply section formula on PQ and find coordinates of S


Therefore, m = 2 and n = 1


P(4, 2, -6) and Q(10, -16, 6)


Coordinates of R using section formula:






Hence, Coordinates of R and S are (6, -4, -2) and (8, -10, 2) respectively


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