If a , b , c , d are unit vectors such that a b = 1 2 , c d = 1 2 and the angle between a b and c d is 6 , then the value of |[ a ~b ~d ] c -[ a ~b c ] d |=

Step-by-step solution

Given E = |[ a b d ] c - [ a b c ] d | , express the scalar triple products using cross and dot products: E = |(( a b ) d ) c - (( a b ) c ) d | . This matches the vector triple product identity X ( Y Z ) = ( X Z ) Y - ( X Y ) Z , with X = a b , Y = c , and Z = d . Thus, E = |( a b ) ( c d )| . Let P = a b and Q = c d . Then E = | P Q | = | P || Q | , where = 6 is given, so = 1 2 . The magnitudes are computed similarly: | a b | = | a || b | ₁ = 1 1 ( 3 ) = 3 2 , since a b = 1 2 implies ₁ = 3 . Likewise, | c d | = |