Given two vectors A and B, we have that the expression to find their dot product is the following:
[tex]\begin{gathered} A=(a_1,a_2,a_3) \\ B=(b_1,b_2,b_3) \\ A\cdot B=a_1b_1+a_2b_2+a_3b_3 \end{gathered}[/tex]
in this case, we have the following vectors:
[tex]\begin{gathered} (3,5,7) \\ (-2,3,-1) \end{gathered}[/tex]
then, their dot product is:
[tex]\begin{gathered} (3,5,7)\cdot(-2,3,-1)=(3)(-2)+(5)(3)+(7)(-1) \\ =-6+15-7=9-7=2 \end{gathered}[/tex]
we have that the dot product between the two vectors is 2.
Since the result of the dot product is not 0, we can confirm that the two vectors (3,5,7) and (-2,3,-1) are not orthogonal
