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.$TkkSnnv3g!!



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irst of all trisect means which divides the line into 3 equal segments....

let  R and S be the two required points...

R divides PQ in the ratio 1:2 and S divides PQ in the ratio 2:1.....

use section formula and get the points

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