Question

If vector a, vector b are two vectors then show that

|vector a + vector b| ≤ | vector a | + | vector b |

Answer 1

= | vector a + vector b |2

= (vector a + vector b)2

=vector a2 + vector b2 + 2 vector a. vector b ≤ | vector a |2 + | vector b |2 + 2 | vector a || vector b |

= (| vector a | + | vector b | )2

= | vector a + vector b | ≤ | vector a | + | vector b |