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

Answer

N/a

Explanation

Let A(x,y,z) and B(p,q,r) be the points trisect PQ.
`because PA=AB=BQ`
`therefore PA : AQ=1 : 2 " and " PB : BQ=2 : 1`
Now, divide PQ in the ratio 1 : 2
`x=(1(10)+2(4))/(1+2)=(18)/(3)=6`
`y=(1(-16)+2(2))/(1+2)=(-12)/(3)= -4`
`z=(1(6)+2(-6))/(1+2)=(-6)/(3) = - 2`
`therefore ` Coordinates of point A=(6,-4,-2)
Again dividing PQ in the ratio 2 : 1
`p=(2(10)+1(4))/(2+1)=(24)/(3)=8`
`q=(2(-16)+1(2))/(2+1)=(-30)/(3)= -10`
`r=(2(6)+1(-6))/(2+1)=(6)/(3)=2`
`therefore` Coordinates of point B=(8,-10,2)
Therefore the coordinates of the points trisecting PQ are (6,-4,-2) and (8,-10,2).