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Dot multiplication

2022-07-21 15:59:00 【51CTO】


                                                                             He zhidan, software architect

Meaning and proof

vector OA Sum vector OB Dot product of . With O Set up a rectangular coordinate system for the origin , Make A The coordinates of the for (x1,y1),B The coordinates of the for (x2,y2).

Then the algebraic meaning of dot multiplication is ：x1x2+y1y2.

The geometric meaning is ：|OA||OB|cos<AOB

Prove algebraic meaning through geometric meaning ：

Through cosine theorem and geometric meaning , We can draw ：

Point multiplication =(OA^2+OB^2-AB^2)/2

=(x1^2+y1^2+x2^2+y2^2-(x1-x2)^2-(y1-y2)^2)/2

=(x1^2+y1^2+x2^2+y2^2-(x1^2-2x1x2+x2^2)-(y1^2-2y1y2+y2^2))/2

=(2x1x2+2y1y2)/2

=x1x2+y1*y2

Physical applications

Work equals Point multiplication of force and displacement

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