Question

Prove that MOD of vector P+Q is less than equal to MOD of vector P + MOD of vector Q ​

Answer 1

|P+Q|= √[|P|^2+|Q|^2+2×|P|×|Q|×cos(@)]

cos(@), max = 1

cos(@), min = -1

|P+Q|, max = √[{|P|+|Q|}^2] = |P|+|Q|

|P+Q|, min = √[{|P|-|Q|}^2] = ||P|-|Q||

so,

|P|+|Q| >= |P+Q| >= ||P|-|Q||