Question

find three points on each plane [x,y,z]= [3,4,-1]+s[1,1,-4]+ t[2,-5,3]

Answer 1

pick any value of s and t you feel like, I will do one

let s = 2, t = 1

(x,y,z) = (3,4,-1) + (2,2,-8) + (2,-5,3) = (7, 1, -6)

Answer 2

why are the answers in the back of my textbook,[3,4,-1], [4,5,-5], [2,3,3]

Answer 3

It said, find three points, that is
any three point from the infinite number of points that would be possible

to get my point, as I said, I let s=2 and t=1

to get their point of (3,4,-1), they used s=0 and t=0
to get their point of (4,5,-5) they used s=1 and t=0

You can use any value of s and t that you want, it was rather silly to even give any answer at all in the back of the book.
It only confuses the student if he/she does not get that particular answer.