2. In this problem, follow the parts to prove the (famous) Triangle Inequality: u + v|...

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2. In this problem, follow the parts to prove the ("famous") Triangle Inequality: │u + v| ≤ |u| + |v| where u and v are vectors. (a) Use the dot product theorem to show that for vectors u and v, |uv|≤|u| |v| This inequality is called the Cauchy-Schwarz Inequality. (b) Sketch a figure and give a geometric interpretation of the Triangle Inequality. (c) Use the Cauchy-Schwarz Inequality to prove the Triangle Inequality. (Hint: Use |u + v2 = (u+v) (u+v), properties of the dot product and the Cauchy-Schwarz Inequality, and take square roots at the end). 2. In this problem, follow the parts to prove the ("famous") Triangle Inequality: │u + v| ≤ |u| + |v| where u and v are vectors. (a) Use the dot product theorem to show that for vectors u and v, |uv|≤|u| |v| This inequality is called the Cauchy-Schwarz Inequality. (b) Sketch a figure and give a geometric interpretation of the Triangle Inequality. (c) Use the Cauchy-Schwarz Inequality to prove the Triangle Inequality. (Hint: Use |u + v2 = (u+v) (u+v), properties of the dot product and the Cauchy-Schwarz Inequality, and take square roots at the end).