Thread: Help with parametric equation

1. Help with parametric equation

Find parametric equations for the line of intersection of the two planes.
P1: 2x − y + z = 1 P2 : x − y + z = 2
<2,-1,1> X <1,-1,1> = <0,-1,1>

x = -1
y=t
z=3+t

I don't know how the book gets this answer.

2. Originally Posted by khuezy
Find parametric equations for the line of intersection of the two planes.
P1: 2x − y + z = 1 P2 : x − y + z = 2
<2,-1,1> X <1,-1,1> = <0,-1,1>

x = -1
y=t
z=3+t

I don't know how the book gets this answer.
Solve simultaneously:

2x − y + z = 1 .... (1)

x − y + z = 2 .... (2)

(1) - (2): x = -1.

Substitute into x = -1 into either (1) or (2):

− y + z = 3.

Now let y = t, say, where $t \in R$ and solve for z.