Your answer is partially correct.

Consider the function $f(x,y)=(e^x-x)cosy.$ 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 $(3,3)$ in the direction in which $f$ decreases most rapidly.

Round your answers to two decimal places.

$($b$)$ Suppose vec$(v)=4$vec$(i)+5$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 $(3,3).$ What is $a?$

Round your answer to two decimal places.

$a=$

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