Here are three displacements, each measured in meters: vec$(d{)}_1=4\mathrm{.}0$hat$()+5\mathrm{.}0$hat$()-6\mathrm{.}0$hat$(k),$vec$(d{)}_2=-1\mathrm{.}0$hat$()+2\mathrm{.}0$hat$()+3\mathrm{.}0$hat$(k)$ and vec$(d{)}_3=4\mathrm{.}0$hat$()+3\mathrm{.}0$hat$()+2\mathrm{.}0$hat$(k).($a$)$ What is vec$(r)=$vec$(d{)}_1-$vec$(d{)}_2+$ vec$(d{)}_3?($b$)$ What is the angle between vec$(r)$ and the positive $z$ axis? $($c$)$ What is the component of vec$(d{)}_1$ along the direction of vec$(d{)}_2?($d$)$ What is the component of vec$(d{)}_1$ that is perpendicular to the direction of vec$(d{)}_2$ and in the plane of vec$(d_1)$ and vec$(d_2)?$