Ahmad B. answered • 01/16/20

PhD in Electrical Engineering with 5+ years of experience

Using the triangular inequality, we know that for any two vectors **a **and **b, **we have

|| **a** + **b **|| ≤ ||**a**|| + ||**b**||

Now notice that || **v** || = || **v** - **w** +** w **||, where we just add and subtract the term **w **then using triangular inequality we get

|| **v** || ≤ || **v** - **w** || + || ** w **||

Now subtract || ** w **|| on both sides, we get

|| **v** || - || ** w **|| ≤ || **v** - **w** ||