A rectangle with sides parallel to the coordinate axes is shown in the figure. Vector vec$(A)$ goes from the origin to the upper left corner of the rectangle, and vector vec$(B)$ goes from the origin to the lower right corner. vec$(A)=8\mathrm{.}50m$ at $50\mathrm{.}0$ from the $+x-$axis, and vec$(B)=12\mathrm{.}0m$ at $29\mathrm{.}0$ from the $+x-$axis.

$($a$)$ Calculate the rectangle's perimeter $($in m $).$

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In the figure, draw a vector from the tip of vec$(A)$ pointing vertically down along the side of the rectangle. Call this $-$vec$(H).$ Then draw a vector going from the tip of $-$vec$(H)$ horizontally to the tip of vec$(B),$ along the bottom of the rectangle. Call this vec$(W).$ Notice that vec$(A)-$vec$(H)+$vec$(W)=$vec$(B).$ You can solve this equation for $-$vec$(H)+$vec$(W),$ calculate vec$(B)-$vec$(A),$ and determine $h$ and $w,$ the components of vec$(H)$ and vec$(W).$ Notice that these are the magnitude of the height and width of the rectangle! Use these values to calculate the perimeter. m

$($b$)$ What are the magnitude $($in m $)$ and direction $($in degrees counterclockwise from the $+x-$axis$)$ of a vector from the origin to rectangle's upper right corner?

$$ m at $-$ counterclockwise from the $+x-$axis

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