Establish the following vector inequalities geometrically or otherwise:
(a) |a + b| β€ |a| + |b|
(b) |a + b| β₯ ||a| β |b||
(c) |a β b| β€ |a| + |b|
(d) |a β b| β₯ ||a| β |b||
When does the equality sign above apply?