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*Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c. *
To find the equation of a plane I need a normal vector and a point. I have the points:

which can give me some vectors. I attached a picture so you can see my reasoning, however it isn't suppose to represent this particular plane. In general:

(1)

* where r may be either vector or and is the vector with terminal point (Note that this notation corresponds to the diagram.)*
If I arbitrarily take

as the terminal point of

, I have

. The vector along

is

, along

, we have

. Using equation (1) I have:

I find the normal vector

using the determinant. I obtain:

(2)

**<<<<<< OK**
(3)

If I plug in any point

into (3), I don't get the correct answer which is:

Where am I going wrong here?