How do you find the normal vector in a point of a sphere?
How do you find the normal vector in a point of a sphere? Sphere with inward normal vector. The sphere of a fixed radius R is parametrized by Φ(θ,ϕ)=(Rsinϕcosθ,Rsinϕsinθ,Rcosϕ) for 0≤θ≤2π and 0≤ϕ≤π. In this case, we have chosen the inward pointing normal vector n=(−sinϕcosθ,−sinϕsinθ,−cosϕ), orienting the surface so the inside is the positive side. How far is a point from a plane? The shortest distance from a point to a plane is along a line perpendicular to the plane. Therefore, the distance from point P to the plane is along a line parallel to the normal vector, which is...