If | a |=2 and | b |=3 and the angle between a and b is 120^ , then the length of the vector | a 2 - b 3 | is

Step-by-step solution

We know that, aligned & a b =| a | | b | & So, a b =(2)(3) 120^ [ =120^ ] & =6 (90^ +30^ )=6 (- 30^ )=-6 1 2 & a b =-3 & Now, | 1 2 a - 1 3 b^2 |^2= ( 1 2 a - 1 3 b ) ( 1 2 a - 1 3 b ) & = 1 4 | a |^2- 1 6 a b - 1 6 a b + 1 9 | b |^2 & = 1 4 4- 1 6 (-3)- 1 6 (-3)+ 1 9 9 & =1+ 1 2 + 1 2 +1=2+1=3 & aligned Hence, option (2) is correct.