- #1
allanwinters
- 5
- 0
Homework Statement
- Does the line with equation (x, y, z) = (5, -4, 6) + u(1,4,-1) lie in the plane with equation (x, y, z) = (3, 0, 2) + s(1,1,-1) + t(2, -1, 1)? Justify your answer algebraically.
Homework Equations
(x,y,z) = (x0,y0,z0) +s(a1.a2,b3) + t(b1,b2,b3)
The Attempt at a Solution
u=-2+s+2t
s=-4 +4u +t
t=4 -u +s
t=4 -(-2 +s+2t) + s, t=-6
s=-4 +4(-2 +s +2(-6)) -6, s=22
u= -2 +22 +2(-6), u=8
(x,y,z) = (5,-4,6) + 8(1,4,-1) = (13,28,-2)
(x,y,z) = (3,0,2) +22(1,1,-1) -6(2,-1,1) =(13,28,-26)
I don't know why the z -coordinate does not match with each other? Does the point not lie in the plane?