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# Understand the problem

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.

# Tutorial Problems!

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 $$\frac{\text{dot product of the coordinates}} {\text{product of their distances from origin}}$$

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