If a , b are two unit vectors with ( a , b )= and | a - b |=1 , then 2| a + b | 2 =

Step-by-step solution

aligned & a , b are unit vectors. So, | a |=1 &| b |=1 & Also, | a - b |^2=1 | a - b |^2=1 & | a |^2+| b |^2-2 a b =1 & 1+1-2 a b =1 a b = 1 2 & | a + b |^2=| a |^2+| b |^2+2 a b =1+1+2 1 2 =3 & | a + b |= 3 & a b =| a | | b | = 1 2 = 1 2 & 2 ^2 2 -1= 1 2 2 ^2 2 = 3 2 ^2 2 = 3 4 & 2 = 3 2 aligned Now, 2| a + b | 2 =2 3 3 2 =3