Equation of a Plane
Two vectors are perpendicular if their directions are 90 degrees apart. The dot product of two perpendicular vectors is zero. A Normal vector to a plane A normal vector to a plane is basically a vector that makes a ninety degree angle with the plane(perpendicular to the plane). In the above picture, \(\vec{d}\) is a normal vector to the plane, P. A normal vector to the plane will be perpendicular to every other vector which is contained in the plane or parallel to the plane. Equation of a plane To find the equation of a plane we need : Any non-zero vector normal to the plane Coordinates of any point in the plane Consider a plane, P. Let there be a point A(-1, -1, 1) in the plane whose coordinates are known to us. Let point B(x, y, z) be an arbitrary point in the plane. It is an arbitrary point, so it could be anywhere on the plane. Let, \(\overrightarrow{d} = -2\hat{i} + 2\hat{j} + 0\hat{k}\) be a normal vector to the plane. The picture below roughl...