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November 23, 2019

Geometry of Cauchy Schwarz Inequality

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Understand the problem

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Cauchy Schwarz Inequality is a powerful tool in Algebra. It was beautiful geometric implications as well. Watch the video and solve the tutorial problems to delve deep into the idea.

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Tutorial Problems!

[/et_pb_text][et_pb_text _builder_version="4.0.6"]1. Look at the expression \( \sqrt{x_1^2 + y_1^2} \times \sqrt {x_2^2 + y_2^2} \geq (x_1 x_2 + y_1 y_2 ) \)  Can you simply square both sides and prove this ? 2. Show that if A, B are any two points in the plane and O is the origin then cosine of the angle AOB is the ratio of $$ \frac{\text{dot product of the coordinates}} {\text{product of their distances from origin}} $$[/et_pb_text][et_pb_text _builder_version="3.27.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" custom_margin="48px||48px" custom_padding="20px|20px|20px|20px" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3"]

Now watch the discussion video

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Subscribe to Cheenta's youtube channel

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Connected Program at Cheenta

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Math Olympiad is the greatest and most challenging academic contest for school students. Brilliant school students from over 100 countries participate in it every year. Cheenta works with small groups of gifted students through an intense training program. It is a deeply personalized journey toward intellectual prowess and technical sophistication.[/et_pb_blurb][et_pb_button button_url="https://www.cheenta.com/matholympiad/" url_new_window="on" button_text="Learn More" button_alignment="center" _builder_version="3.23.3" custom_button="on" button_bg_color="#0c71c3" button_border_color="#0c71c3" button_border_radius="0px" button_font="Raleway||||||||" button_icon="%%3%%" background_layout="dark" button_text_shadow_style="preset1" box_shadow_style="preset1" box_shadow_color="#0c71c3"][/et_pb_button][et_pb_text _builder_version="3.27.4" text_font="Raleway|300|||||||" text_text_color="#ffffff" header_font="Raleway|300|||||||" header_text_color="#e2e2e2" background_color="#0c71c3" custom_margin="50px||50px" custom_padding="20px|20px|20px|20px" border_radii="on|5px|5px|5px|5px" box_shadow_style="preset3"]

Similar Problems

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