I'm not too sure what I should've put as the title...
My teacher presented the class with a question that any of us has yet to solve.
Show that the plane that passes through the axis at , , and is described by the equation,
I have absolutely no idea how to approach this question and would appreciate any suggestions.
Hello, deovolante!
Show that the plane that passes through the axes at , ,
is described by the equation: .
The equation of a plane has the form: . .[1]
Substitute the three given intercepts:
. .
And we have: .
Substitute into [1]: .
Divide by
Therefore: .
You are not asked to derive the equation of the plane, just to show that this is the equation of that plane.
Since is linear in each variable, it represents a plane.
If x= a, y= 0, z= 0, then so the plane contains (a, 0, 0).
If x= 0, y= b, z= 0, then so the plane contains (0, b, 0).
If x= 0, y= 0, z= c, then so the plane contains (0, 0, c).
Since a plane is determined by three points, this is the required plane.