vectors
posted by sara on .
find three points on each plane [x,y,z]= [3,4,1]+s[1,1,4]+ t[2,5,3]

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

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.