Line and Inner Product(Dot Product)


Introduction

Vector OA and the green line cross perpendicularly. Point B is on the line. Point P can move freely. When point P moves with keeping constant value of inner product (dot product) of vector OA and OP, the trace of point P is the line.
Then,we define = , = .
=

= ax + by = const.

This expression means the line .
Reference:Inner product (Dot product).

Applet

How to use this applet

  • Drag red point.
  • Press [Next] button.
  • Check [Area].
  • Check [Vector BP].
  • Check [Projective vector]
  • Check [P:Free].
  • Check [Line].
  • Press [Init] to go to the first step.