- #1
Andrew Pierce
- 8
- 0
Homework Statement
Two planes are given by the equations x + y + z = 1 for the plane P1 and x − y + z = 1 for the plane P2.
(or)
P1 : x + y + z = 1
P2 : x - y + z = 1
Q. The Question
Find the coordinates of a point of intersection of the planes P1 and P2
Homework Equations
Equation of a plane
Ax + By + Cz + D = 0
Parametric equations
x = xo + at
y = yo + bt
z = zo + ct
Possibly using cross product?
P1 x P2 ?
The Attempt at a Solution
Attempt 1:
So to start off I thought maybe finding the line of intersection would be the way to go about solving this problem, and then working from there to find some point.
Rewrite P1 and P2 to give the variable "x" on one side of the equation
P1 : x = 1 - y - z
P2 : x = 1 + y - z
Then setting both of the "x" variables equal to each other.
1 - y - z = 1 + y - z
Then I solve for "y"
y = 0
And now I'm lost.
Attempt 2:
Then I attempted to do what I normally did for trying to find any equations that intersect by setting the two equations equal to each other.
P1 = P2
x + y + z = x - y + z
And then I'm right back to where I started...
y = 0
Attempt 3:
Finally, I remembered a bit of information from a lecture from my professor about how using the cross product and setting a variable equal to zero was the way to go. Unfortunately, I do not have any detailed notes on the procedure and don't remember any more than that. P1 x P2 = < 2, 0, -2>