If a = 1 10 (3 i + k ) and b = 1 7 (2 i +3 j -6 k ) then the value of (2 a - b ) (( a b ) ( a +2 ~b ))=

Step-by-step solution

Given the expression E = (2 a - b ) (( a b ) ( a + 2 b )) , applying the vector triple product identity ( X Y ) Z = ( X Z ) Y - ( Y Z ) X with X = a , Y = b , Z = a + 2 b yields: ( a b ) ( a + 2 b ) = (| a |^2 + 2( a b )) b - (( a b ) + 2| b |^2) a Substituting back and computing the dot product with 2 a - b gives: E = (2K₁ + K₂)( a b ) - 2K₂| a |^2 - K₁| b |^2 where K₁ = | a |^2 + 2( a b ) and K₂ = a b + 2| b |^2 . After substitution and simplification, terms cancel to yield: E = 5[( a b )^2 - | a |^2| b |^2] Give