Q $2$ Let $f(x,y)=7-x^2-3y^2.$ Find a vector:

$($a$)$ perpendicular to the level curve of $f$ at the point $(-1,1).$

$($b$)$ perpendicular to the surface $z=f(x,y)$ at the point $(-1,1,3).$

$($c$)$ tangent to the curve of steepest ascent $($increase$)$ on the surface $z=f(x,y)$ at the point $(-1,1,3)$