This is the formula http://www.mathsmutt.co.uk/files/vec3_files/Eqn54.gif
The equation d = (|Ax+By+Cz+D|)/(sqrt(A^2 + B^2 + C^2)) gives is the distance between a plane and a point as the value 'd'. What is the unit of this value? Why is the distance between the plane and the point not a vector?
~Thanks!
On
Distances have units of length. You can see this from the formula, where the numerator has units like $Ax$ and the denominator has units like $A$, so the ratio has units of $x$. You can certainly define a vector from the point to the nearest point on the plane, but that is not this formula. This formula gives the magnitude of that vector.
The equation $\displaystyle d = \frac{|Ax+By+Cz+D|}{\sqrt{A^2 + B^2 + C^2}}$ gives us the distance a point from a plane in $\mathbb{R}^3$. Here we discuss about Euclidean space and distances measured by physical units, here obey on $x$, $y$ and $z$ and $A$, $B$, $C$ and $D$ are constant scalars belong to $\mathbb{R}^3$ without units. Then the unit of $d$ is the same as variables have.
Also, the distance is not a vector, it is the smallest way between the point and a point on plane measured without direction.