Scalar versus linear equation of a plane What is the difference between a scalar and a linear equation of a plane? In my textbook it says that a scalar equation is $a(x-x_1)+b(y-y_1)+c(z-z_1)=0$
and a linear equation is $ax+by+cz=d$
How do they differ in terms of what they describe?
If a line on the plane dot the normal vector $= 0$ why do we have $d$ for the linear equation?

The equation $a(x-x_1)+b(y-y_1)+c(z-z_1)=0$ means that a vector $\vec x -\vec x_1$ is orthogonal to the vector $\vec v =(a,b,c)^T$, so it represents the plane orthogonal to $\vec v$ and passing thorough $\vec x_1$. It is the same as $ax+by+cz=d=ax_1+by_1+cz_1$. 
The first form ( ''scalar") shows immediately a point between wich passes the plane, the second form (''linear'') shows the intercepts of the plane with the coordinates axis $ (d/a,d/b,d/c)$. 
