Calculus 3 | 8.1: The Equation of a Plane from a Point and Normal Vector

Full course — free exercises, Feynman reviews, and AI-graded feedback: https://ludium.ai/courses/calculus-3 A single point and a single arrow pointing straight out of a surface are all it takes to lock a flat plane into three-dimensional space. In this video we build the equation of a plane from exactly those two ingredients, a point on the plane and a normal vector, then use it to write a plane parallel to one we are handed. Key concepts covered: What a normal vector is, and why one normal is enough to fix a plane's orientation Why a point plus a normal vector determine exactly one plane How a plane differs from a line: same ingredients, opposite role for the vector Deriving the plane equation from the dot product condition N dotted with the in-plane vector equals zero Standard form and general form of the equation of a plane Writing the equation of a plane parallel to a given plane