If a = 1 10 (4 i -3 j + k ), b = 1 5 ( i +2 j +2 k ) , then the value of (2 a - b ) ( a b ) ( a +2 b ) is

Step-by-step solution

a and b are perpendicular unit vectors. aligned & Now, (2 a - b ) ( a b ) ( a +2 b ) & =[2 a - b a b a +2 b ] & =-[ a b 2 a - b a +2 b ] & =-( a b ) (2 a - b ) ( a +2 b ) aligned aligned & =-( a b ) 5( a b ) & =-5| a b |=-5| a |^2| ~b |^2 & =-5 aligned aligned & [ a b ] & [ | a |=| b |=1] aligned