Find the equation of the plane passing through the points (-1,1,1) and (1,-1,1) and perpendicular to the plane x+2y+2z=5 ?
1 Answer
Explanation:
We can find the Cartesian equation of a plane by the following:
If we have 3 points in a plane: A, B, C. Then for some point P in the plane with co-ordinates
Where
If we find a vector normal to the given plane, and this vector be in the plane we seek, then we have a vector in the plane and the 2 given points that lie in the plane.
This normal vector can be found easily from the given equation of the plane.
The normal vector is:
The proof of this can be found here:
https://socratic.org/questions/5a7899f37c01495f160bbd53#547058
Let the given points be:
and the normal vector:
Another vector in the plane could be:
and we have:
So:
Form the following equations:
We need to eliminate
Add
From
Substitute in
This is the equation of the plane perpendicular to:
PLOT: