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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?