Vector vec$(A)$ has a magnitude of $11\mathrm{.}7$ units and points due west. Vector vec$(B)$ points due north. $($a$)$ What is the magnitude of vec$(B)$ if vec$(A)+$vec$(B)$ has magnitude of $18\mathrm{.}8$ units? $($b$)$ What is the direction of vec$(A)+$vec$(B)$ relative to due west? $($c$)$ what is the magnitude of vec$(B)$ if vec$(A)-$vec$(B)$ has a magnitude of $18\mathrm{.}8$ units? $($d$)$ What is the direction of vec$(A)-$vec$(B)$ relative to due west?

$($Note: Use the convention that an angle north of west is positive, and an angle south of west is negative.$)$

$($a$)$ Number Units

$($b$)$ Number

Units

$($c$)$ Number Units

$($d$)$ Number Units