Consider the function $f(x,y)=(e^x-5x)sin(y).$ Suppose $S$ is the surface $z=f(x,y).$

$($a$)$ Find a vector which is perpendicular to the level curve of $f$ through the point $(1,3)$ in the direction in which $f$ decreases most rapidly. vector $=$

$($b$)$ Suppose vec$(v)=7$vec$(i)+8$vec$(j)+$avec$(k)$ is a vector in $3-$space which is tangent to the surface $S$ at the point $P$ lying on the surface above $(1,3).$ What is $a?$

$a=$