$(2pts)$ Let $z=f(x,y)be$ a smooth function with gradf$(1,2)=3$vec$(i)+4$vec$(j).$

$(a)$ Compute the directional derivative $f_{\text{v}\text{e}\text{c}(u)}(1,2),$ where vec$(u)is$ shown $in$ Figure $1(II).$

$(b)$ Refer $to$ Figure $1(III)$ for gradf$(1,2)$ and vec$(v).$ Suppose the directional derivative $f_{\text{v}\text{e}\text{c}(v)}(1,2)=2\mathrm{.}5.$

Determine the angle $between$ gradf$(1,2)$ and vec$(v).$

Figure $1.$ Figures for Problem $1$ and Problem $2.$

$(2pts)$ Vectors vec$(a),$vec$(b),$vec$(c),$ and vec$(w)=$grad${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(Q)$ are shown $in$ Figure $1(I).$ Arrange the directional

derivatives $f_{\text{v}\text{e}\text{c}(a)}(Q),f_{\text{v}\text{e}\text{c}(b)}(Q),$ and $f_{\text{v}\text{e}\text{c}(c)}(Q)in$ ascending order $(from$ smallest, $to$ largest$)$ :