(2) For any two vectors u and v, the inequality u . v|

(2) For any two vectors u and v, the inequality lu vl Ilull Ilvll is called Cauchy- Schwarz Inequality. (a) Use the Cauchy-Schwarz Inequality to show that for any two positive numbers a and b, we have < Hint: Use a and b to define two vectors and apply the 2 inequality. (b) Prove that without using the Cauchy-Schwarz Inequality. 2 (c) Use the Cauchy-Schwarz Inequality to show the triangle inequality