Equation of Plane Passing Through Two Points Parallel to x-axis

[economics]

Homework Statement

Plane passes through points (a,b,c) and (e,f,g) parallel to x-axis
Find the equation of plane Ax+By+Cz+D=0
General question for this--(a,b,c) and (e,f,g) can be any points in space

Homework Equations

Below

The Attempt at a Solution

First, I find the vector <e-a,f-b,g-c>
Then, I know parallel to x-axis implies that direction vector is <1,0,0>
Next, I do cross product between first vector and second vector. I would then get <i,j,k>.
So, how do i use this information to get equation of the plane? Do i use <i,j,k> from cross product as A,B,C, in the equation of the plane? How do I find D? Is this attempt even correct?

Thanks for any info. Calc III is awesome!

 

[Dick]

Calc III is awesome!

At least you have a positive attitude towards the material! Yes, you are on the right track. The cross product of the direction vectors is a normal to the plane. And that gives you A, B and C. To find D, you put a point on the plane like <a,b,c> or <d,e,f> into the equation for x, y and z and solve for D.

 

[economics]

Thanks again for the solutions. I figured the problem out with your assistance.