If a and b are two unit vectors such that a +2 ~b and 5 a -4 b are perpendicular to each other, then the angle between a and b is

Step-by-step solution

Let be the angle between a and b . Since c = a +2 ~b and d =5 a -4 ~b are perpendicular to each other. aligned & c ~d =0 & ( a +2 ~b ) (5 a -4 ~b )=0 & 5( a a )+6( a ~b )-8( ~b ~b )=0 & 5| a |^2+6| a || b | -8| ~b |^2=0 & 5+6 -8=0 & = 1 2 & = 3 aligned