Find the coordinates of the points which trisectthe line segment `A B ,`given that `A(2,1,-3)n d B(5,-8,3)dot`

Find the coordinates of the points which trisectthe line segment `A B

1.	Find the coordinates of the points which trisectthe line segment `A B ,`given that `A(2,1,-3)n d B(5,-8,3)dot`
Answer» 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)

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