Let u → be a vector coplanar with the vectors a → = 2 i ^ + 3 j ^ - k ^ and b → = j ^ + k ^ . If u → is perpendicular to a → and u → ⋅ b → = 24 , then u → 2 is equal to:

Step-by-step solution

As u → = λ [ a → × ( a → × b → ) ] u → = λ [ [ a → . b → ] a → − | a → | 2 b → ] u → = λ [ 2 a → − 14 b → ] u → . b → = 2 λ [ a → .   b → − 7 | b → | 2 ] = 2 λ [ 2 − 14 ] 24 = − 24 λ λ = − 1 u → = 14 b → − 2 a → u → = - 4 i ^ + 8 j ^ + 16 k ^ | u → | 2 = 4 2 + 8 2 + 16 2 = 336