HOW TO MATHS A-Levels: Mini Crash Course PLANES | Vector Calculus
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Plane equation
Using vectors, you can create an equation that describes a plane: This creates the vectorial form of a plane equation. In this video, I'll show you the basic principle of a vector plane equation and how you can create a plane from three points. Have fun, Your Rick :)
--------SUMMARY-----------------------------
BASIC PRINCIPLE:
A plane equation can be interpreted as a linear combination of a support vector and a direction vector.
STRAIGHT LINE FROM 3 POINTS:
As the support vector, choose the position vector of any point in the plane. As the direction vectors, choose any two (linearly independent) vectors in the plane.
POINT TEST:
To check whether a point lies in a plane, substitute the components of the position vector for vector x and check whether the same parameter values result in all components.
This leads us to a system of equations. Since this can sometimes be time-consuming, we'll introduce the coordinate form of a plane at this point.
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