The Cauchy Schwartz Inequality states that :   |<u, v>| ≤ ||u|| ||v||

Refer the figure on right Let u = and v = , then |<u, v>| = Area of rectangle OEDC ||u|| ||v|| = Area of rectangle OFGC Referring the figure, we can observe that          |<u, v>| ≤ ||u|| ||v||

Instructions for using the Applet Click on the display panel to generate two vectors u and v Click on one of the two buttons Show |<u, v>| or Show ||u|| ||v|| to see the respective operations Click on the |<u, v>| ≤ ||u|| ||v|| button to check the truth of the inequality (this activates only after checking first two operations) You may drag any of the vectors to change them holding their arrow heads Click on the Reset button to reset the applet