Find the coordinates of the points which trisect the line segment `A B ,` given that `A(2,1,-3)` and `B(5,-8,3)`

Explanation

Let the P `(x_(1)y_(2),z_(1) and Q (x_(2),y_(2),z_(2))` trisect line segment AB.
`(2,1,-3) (x_(1),y_(1),z_(1)),(x_(2),y_(2),z_(2)) (5,-8,3)`
Since , the point P divded line AB in 1:2 internally then
`x_(1)=(2xx2+1xx5)/(1+2)=9/3=3`
`y_(1)=(2xx1+1xx(-8))/3= -(-6)/3=-2`
`z_(1)=(2xx(-3)+1xx3)/3= (-6+3)/3= (-3)/3=-1`
Since the point Q divide the line segment AB in 2:1 then
`x_(2)=(1xx2+2xx5)/3=4`
`y_(2)=(1xx1+(-8xx2))/3=-5`
`z_(2)=(1xx(-3)+2xx3)/3=-1`
So, the coordinates of P are ( 3,-2,-1) and the corrdinates of Q are (4,-5,1)