Triangle Inequality Consider the vectors u, v, and u + v
Chapter 11, Problem 87(choose chapter or problem)
Triangle Inequality Consider the vectors u, v, and u + v (in any number of dimensions). Use the following steps to prove that _ u + v _ _ u _ + _ v _. a. Show that _ u + v _2 = 1u + v2 # 1u + v2 = _ u _2 + 2u # v + _ v _2. b. Use the CauchySchwarz Inequality to show that _ u + v _2 1_ u _ + _ v _22. c. Conclude that _ u + v _ _ u _ + _ v _. d. Interpret the Triangle Inequality geometrically in _2 or _3. 8
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