Find the coordinates of the points which trisect the line segment joining the points P (4, 2, –6) and Q (10, –16, 6).
This is an exercise question(ex 12.3,Q-5)

couldn't we do the same problem like this:

if it is a trisect then first we can find the mid point of PQ,say R

And then wouldn't the midpoint of R&P,R&Q be the points required????

huh????

No, the problem can not be solved by the method given by you. 

The given point are P(4, 2, – 6) and Q(10, – 16, 6)

Let A and B trisects the line segment PQ.

∴ PA = AB = BQ

AQ = AB + QB = PA + PA = 2PA

PA : AQ = AP : 2AP = 1 : 2

∴ A divides the line segment PQ in the ratio 1 : 2.

Similarly, B divides the line segment PQ in the ratio 2 : 1.

The complete answer to the question is given at the following link.

http://cbse.meritnation.com/study-online/solution/math/mYH0c@IOfXwT$TkkSnnv3g!!