# Homework Help: Proving the line lies on the plane

1. Mar 29, 2009

### soulja101

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. The attempt at a solution
I started by getting the parametric equation of (x, y, z) = (5, -4, 6) + u(1,4,-1)
x=5+u
y=-4+4u
z=6-u
I then subbed in u=0 to get a set of points
x=5
y=-4
z=6

I then got the parametric equation for (x, y, z) = (3, 0, 2) + s(1,1,-1) + t(2, -1, 1)
x=3+s+2t
y=0+s-t
z=2-s+t

I decided to use the points (5,-4,6)

2. Mar 29, 2009

### tiny-tim

Hi soulja101!
This is very long-winded

you could just put u = 0 in (x, y, z) = (5, -4, 6) + u(1,4,-1), giving (5, -4, 6) immediately
why make it so complicated?

all you have to prove is that (5, -4, 6) minus (3, 0, 2) is a linear combination of (1,1,-1) and (2, -1, 1), and then the same for (1,4,-1)