The difinition of Inner Product is
|
|
.
|
It is represented by the area of the rectangle.
If cos t>0,the sign of the area sign is "+",and if cos t<0,then "-".
|
|
Next, we transform the rectangle into the parallelogram as the right figure without changing the area.
Let |
|
=(Ax,Ay) and |
|
=(Bx,By).
|
The area of the rectangle is equal to the area of the parallelogram created by vector(Ay,-Ax) and (Bx,By).So,the area is AxBx+AyBy.
|
|
=AxBx+AyBy
|
Please refer to the applet"The Area of a Parallelogram (1)" or "The Area of a Parallelogram (2)".
|
|