) Given the vectors 𝑎=(1,2,3) a = ( 1 , 2 , 3 ) and 𝑏=(1,−1,2) b = ( 1 , − 1 , 2 ) , what is the dot product 𝑎⋅𝑏⋅𝑎 a ⋅ b ⋅ a ?

Question

) Given the vectors  and , what is the dot product ?

Answer 1

This is an interesting question. It is not clear what they are looking for here. The dot product is a binary operation, which means that it takes two vectors and gives one output (namely, a scalar). The problem is that the dot product cannot be performed on three vectors simulaneously - this is the reason the dot product is not associative: because it would not be defined (you'd be trying to find the dot product of a scalar with a vector). So, no matter which two vectors you begin with, you won't be able to find an answer.