a and b are unit vectors such that a +2 b is also a unit vector. If is the angle between a and b , then + ^3 + ^5 is equal to

Step-by-step solution

aligned & Given, | a |=| b |=| a +2 b |=1 & aligned | a +2 b |^2 & =| a |^2+4 | b ^2 |+4| a || b | 1 & =1+4+4 & =-1 = & + ^3 + ^3 & = + ^3 + ^3 =0 & +(-1)^3+0=-1 aligned aligned