Write scalar equations of planes

A plane in three-dimensional Cartesian space is represented by a scalar equation $ax+by+cz=d$, where $(a,b,c)\neq(0,0,0)$ is a normal vector and every point $(x,y,z)$ on the plane satisfies the equation. From a point and a normal vector, or from geometric information such as a point and two nonparallel directions (using a cross product to obtain a normal), one can construct an equivalent equation; multiplying all coefficients by the same nonzero constant does not change the plane.