|Applet 7.3 Distribution law of Inner Product|
The Distribution law of inner product states that :
|<u + v, w>| =
|<u, w>| + |<v, w>|
Refer the figure on right
Let u = , v = , and w =
So, u + v =
Referring the figure on the right, we observe that
|<u + v, w>| = Area of rectangle OPHC'
|<u, w>| = Area of rectangle OEDC'
|<v, w>| = Area of rectangle OFGC'
Now as area of OPHC' = area of OEDC' + area of OFGC'
(which can be checked with the help of the applet below using the Check button)
|<u + v, w>| = |<u, w>| + |<v, w>|
Instructions for using the Applet