In a previous Quora post on this topic (), a respondent states that $D$ represents the distance from the origin to a plane. In a similar post on this site (What does the d represent in the equation of a plane ($ax+by+cz+d=0$)?), it was said that changing the value of $D$ results in translating/sliding the plane.
But since $D$ is a number and not a vector, how can we know in which direction this distance is measured? Is it just a case of positive $D$ resulting in translation to the right, along the $x$ (horizontal) axis, and negative $D$ resulting in translation to the left?
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$\begingroup$You can view $ax+bx+cz$ as the scalar product of vectors $(x,y,z)$ and $(a,b,c)$, and the plane equation says that this scalar product is $-d$. So if $(a,b,c)$ is a vector of unit length, then our plane consists of all points on the plane perpendicular to $(a,b,c)$, translated by $-d$ units in the direction of vector $(a,b,c)$.
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