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If we are to write the equation of a variable plane that passes through the point $(a,b,c)$ then can we say the general equation of the plane will be $\dfrac xa+\dfrac yb+\dfrac zc=3$? Or would it be some specific plane only and not a general one?

I understand that the equation of a plane in general is $Ax+By+Cz+D=0$, or in the intercept form, it is $\dfrac xA+\dfrac yB+\dfrac zC=1.$

aarbee
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    It would be a specific plane, since you are choosing specific values for $A,B,C,D$, namely $A=\frac{1}{a}$, $B=\frac{1}{b}$, $C = \frac{1}{c}$, and $D = -3$. You would need more variables (degrees of freedom) to describe a "generic" plane passing through the given point. – Nick Jun 13 '21 at 20:03

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$\frac {x}{a} + \frac {y}{b} + \frac {z}{b} = 3$ is a specific plain.

As $Ax + By + Cz + D = 0$ is the general equation of a plane. The point on the plane $(a,b,c)$ will determine the value of $D.$

Specifically, $Ax + By + Cz - (Aa + Bb + Cc) = 0$

Doug M
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