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>|
                 		 Distributive.png
        Instructions for using the Applet
        1. Click on the display panel to generate three vectors u, v and w
        2. Click on one of the three buttons
          Show |<u, w>|,
          Show |<v, w>| or
          Show |<u + v, w>| to see their respective operations
        3. Click on the Check button to check the truth of the equality
          (This activates only after checking first three operations)
        4. You may drag any of the vectors to change them holding their arrow heads
        5. Click on the Reset button to reset the applet

Reload Applet

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