Answer
(i) matches Figure (A)
(ii) matches Figure (B)
Work Step by Step
(i) We have $f\left( {x,y} \right) = \left( {\cos x} \right)\left( {\cos y} \right)$. By setting $y=a$ we fix the $y$-coordinate and obtain the vertical trace curve $f\left( {x,a} \right) = z = \left( {\cos x} \right)\left( {\cos a} \right)$ that lies in the plane parallel to the $xz$-plane. So, it matches Figure (A).
(ii) We have $f\left( {x,y} \right) = \cos \left( {{x^2} + {y^2}} \right)$. By setting $y=a$ we fix the $y$-coordinate and obtain the vertical trace curve $f\left( {x,a} \right) = z = \cos \left( {{x^2} + {a^2}} \right)$ in the plane parallel to the $xz$-plane. So, it matches Figure (B).
