# Determine Cartesian eq given

## Homework Statement

Determine the Cartesian equation for the plane with the following:
1) through the points (1,2,1) and (2,1,4)
2) parallel to x-axis

## Homework Equations

Parametric Equations
Vector Eqs
Plane Eqs

## The Attempt at a Solution

I basically understand how perpendicular works, but not sure how paralell will change this situation. I know that I will get a direction vector out of this from the first two points, which will be (1,-1,3), but then I don't know what to do after..

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LCKurtz
Homework Helper
Gold Member
OK, you have so far that D = <1,-1,3> is in the plane, so it is perpendicular to the plane's normal, call it N. If (x,y,z) is a variable point in the plane you can make another vector in the plane and perpendicular to the plane's normal N.

So the problem boils down to what does the normal vector N to the plane look like if the plane is parallel to the x axis? What can you say about its components?

HallsofIvy
If a plane is parallel to the x-axis, then the vector $\vec{i}$, or (1, 0, 0) in your notation, is in the plane. Use the two given points to find another vector in the plane and take their cross product to get a vector normal to the plane.