$7\mathrm{.}9($a$)$ For the following surface

$z=f(x,y)=3-x^2-2y^2$

find all the directions at point $)=0\mathrm{.}5,y=(0\mathrm{.}5$ with slope equal to $1\mathrm{.}0$ or $-1\mathrm{.}0.$

$($b$)$ Plot the directional vectors on the filled color contour map. Since the unit vectors are too long to fit the figure, you can plot only $30\%$ or $20\%$ of the vector's length.

Please use R studio code and provide the code.