How To Find The Equation of a Plane Given a Point and Perpendicular Normal Vector  Summary and Q&A
TL;DR
Learn how to find the equation of a plane using a given point and a vector that is perpendicular to the plane.
Questions & Answers
Q: What are the two things needed to define a plane?
A point on the plane and a vector that is perpendicular to it.
Q: How can you determine if two vectors are orthogonal or perpendicular?
If the dot product of the two vectors equals zero, they are orthogonal or perpendicular to each other.
Q: How do you find the equation of a plane using a point and normal vector?
Using the formula A(X  X0) + B(Y  Y0) + C(Z  Z0) = 0, where A, B, and C are the components of the normal vector, and X0, Y0, and Z0 are the coordinates of the point.
Q: Can you provide an example of finding the equation of a plane?
Let's say A is 3, B is 6, C is 5, X0 is 2, Y0 is 5, and Z0 is 3. Plugging these values into the formula, we get 3x + 6y + 5z = 9 as the equation of the plane.
Summary & Key Takeaways

To define a plane, you need a point on the plane (P0) and a vector (N) that is perpendicular to it.

The dot product of the normal vector (N) and the vector from P0 to any other point on the plane (R  R0) equals zero.

Using the formula, A(X  X0) + B(Y  Y0) + C(Z  Z0) = 0, you can find the equation of the plane.