SOLUTION:

(a,b,c)Θ(d ,e, f)=ad+ be +cf

In the expression (1,−2,3)Θ(1,−1/2,1/3) ,
a=1 d=1
b=-2 e=-1/2
c=3 f= 1/3


Using this operation, we have, ad+ be +c f

= (1.1) + (-2. -1/2) + (3.1/3)

= 1 + 1 +1

=3 (OPTION E)