- #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?