Can you write the general equation of a tangent plane as a dot product?
If you take the cross product of the two directional vectors of the plane v and w (they lie in the plane), you will get a vector that is orthogonal to both of them. That vector is the normal vector n. We also have a point in the plane, the point of tangency R1. With a point in the plane and a normal vector to the plane we can write the equation of the plane. Remember, the normal vector is orthogonal to any vector that lies in the plane. And the dot product of orthogonal vectors is zero. Define R to be an arbitrary point in the plane. Then vector R1R lies in the plane and is orthogonal to n. Therefore we have an equation of the plane. n • R1R = 0 n •
