This is a vector inequality from Michael Corral's text Vector Calculus. http://www.mecmath.net/ Problem 1.3.24 Prove | ||[b]v[/b]|| - ||[b]w[/b]|| | <= || [b]v[/b] - [b]w[/b]|| for all [b]v[/b] and [b]w[/b].
1. When does equality hold? 2. Does equality always hold when v and w are on the same line? 3. What are the exact conditions on u and v for equality?