Final answer:
The equation of a plane is determined using a known point and a normal vector, obtainable by the cross product of two vectors lying on the plane.
Step-by-step explanation:
The equation of a plane can be determined when we know a point through which the plane passes and a normal vector that is perpendicular to it. To find the normal vector, we can use cross products of vectors that lie in the plane.
For instance, if vectors A and B lie in the plane, their cross product A x B will give us the normal vector. Once we have a normal vector, say n with components nx, ny, and nz, and a known point P(x0, y0, z0), the equation of the plane can be given by nx(x - x0) + ny(y - y0) + nz(z - z0) = 0, where (x, y, z) are the coordinates of any point on the plane.