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????
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.