Let a and b be the vectors of the same magnitude such that | a + b |+| a - b | | a + b |-| a - b | = 2 +1 . Then | a + b |^2 | a |^2 is :

Step-by-step solution

| a + b |+| a - b | | a + b |-| a - b | = 2 +1 Apply componendo and dividendo aligned & 2| a + b | 2| a - b | = 2 +2 2 & | a + b |=(1+ 2 )| a - b | & | a + b |^2=(3+2 2 )| a - b |^2 & 2| a |^2+2 a ~b =(3+2 2 ) (2| a |^2-2 a ~b ) & 2| a |^2(2+2 2 )=2 a ~b (4+2 2 ) & a ~b | a |^2 = 2+2 2 4+2 2 = 1 2 aligned Now aligned & | a + b |^2 | a |^2 =1+ | b |^2 | a |^2 + 2 a ~b | a |^2 & =1+1+2 ( 1 2 )=2+ 2 aligned