What is the equation of the plane that contains the triangle shown in the diagram?

2x + 3y + z = 6

2x + 3y + 6z = 12

3x + 2y + 6z = 0

6x + 2y + 3z = 18

Question

What is the equation of the plane that contains the triangle shown in the diagram?
  

       2x + 3y + z = 6

       2x + 3y + 6z = 12

       3x + 2y + 6z = 0

       6x + 2y + 3z = 18

anonymous · Answer

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tkhunny · Answer

It is a beautiful application of the Intercept Form.

Given the intercepts (3,0,0)(0,2,0)(0,0,6), we simply write down the equation of the plane.

$\dfrac{x}{3} + \dfrac{y}{2} + \dfrac{z}{6} = 1$

It is a beautiful thing, indeed.  Too bad hardly anyone I have met has even heard of the Intercept Form.