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.
To find three points on the plane described by the equation [x, y, z] = [3, 4, -1] + s[1, 1, -4] + t[2, -5, 3], we need to substitute different values for s and t. By doing so, we can find the corresponding values of x, y, and z.
Let's find the points step by step:
1. Set s = 0 and t = 0:
[x, y, z] = [3, 4, -1] + 0[1, 1, -4] + 0[2, -5, 3]
Simplifying, we get:
[x, y, z] = [3, 4, -1]
So, the first point on the plane is (3, 4, -1).
2. Set s = 1 and t = 0:
[x, y, z] = [3, 4, -1] + 1[1, 1, -4] + 0[2, -5, 3]
Simplifying, we get:
[x, y, z] = [4, 5, -5]
The second point on the plane is (4, 5, -5).
3. Set s = 0 and t = 1:
[x, y, z] = [3, 4, -1] + 0[1, 1, -4] + 1[2, -5, 3]
Simplifying, we get:
[x, y, z] = [5, -1, 2]
The third point on the plane is (5, -1, 2).
So, the three points on the plane are (3, 4, -1), (4, 5, -5), and (5, -1, 2).