Definition of the dot product in the two-dimensional space The definition of the dot product of two vectors \(u = (u_1,u_2)\) and \(v = (v_1,v_2)\), denoted by \( u \cdot v \), is as follows: $$ u \cdot v = u_1 v_1 + u_2 v_2. $$ Example. Let us compute the dot product of \(u…