A proton initially has vec$(v)=(3\mathrm{.}20)hat(i)+(-8\mathrm{.}60)hat(j)+(8\mathrm{.}10)hat(k)$ and then $2\mathrm{.}10$ s later has vec$(v)=(-6\mathrm{.}00)hat(i)+(-8\mathrm{.}60)hat(j)+(5\mathrm{.}20)hat(k)($in meters per second$).($a$)$ For that $2\mathrm{.}10s,$ what is the proton's average acceleration vec$(a{)}_{\text{a}\text{v}\text{g}}$ in unit vector notation, $($b$)$ in magnitude, and $($c$)$ the angle between vec$(a{)}_{\text{a}\text{v}\text{g}}$ and the positive direction of the $x$ axis?

$($a$)$ Number

hat$(i{)}^{+}$ widehat$(k)$ Units

$($b$)$ Number Units

$($c$)$ Number Units