$6$ Bees and vectors

Consider a bee foraging for nectar by going to various flowers in a field near its hive. Suppose that the bee starts at the hive and visits three flowers along its route. Let our $\backslash ($ y $\backslash )$ versus $\backslash ($ x $\backslash )$ coordinates of locations have $\backslash ((0,0)\backslash )$ as the location of the hive, with $\backslash ($ y $\backslash )$ representing the North$-$South axis $($positive and negative $\backslash ($ y $\backslash ))$ and $\backslash ($ x $\backslash )$ representing the East$-$West axis $($positive and negative $\backslash ($ x $\backslash )),$ respectively.

$-$ Flower $1$ which is $\backslash (45^\{\backslash$circ$\}\backslash )$ counterclockwise away from the positive $\backslash ($ x $\backslash )$ axis $($East$),$ at a distance of $150$ meters from the hive.

$-$ Flower $2$ is $\backslash (105^\{\backslash$circ$\}\backslash )$ clockwise away from the positive $\backslash ($ x $\backslash )$ axis $($East$),$ at a distance of $200$ meters from the hive.

$-$ Flower $3$ is in the negative $\backslash ($ x $\backslash )$ direction $($West$),$ a distance of $400$ meters from the hive.

$($a$)$ Sketch the locations of the three flowers and the hive on a $\backslash ($ y $\backslash )$ versus $\backslash ($ x $\backslash )$ plot.

$($b$)$ What would be the total displacement vector $\backslash (\backslash$Delta $\backslash$mathbf$\{$x$\}\_\{\backslash$text $\{$hive $\}\backslash$rightarrow $3\}\backslash )$ of the bee for its motion from the hive, to flower $1,$ to flower $2,$ and finally ending up at flower $3?$ Write your answer in the vector notation $\backslash (\backslash$binom$\{\backslash$Delta x$\}\{\backslash$Delta y$\}\backslash )$ with the appropriate $\backslash ($ x $\backslash )$ and $\backslash ($ y $\backslash )$ components.

$($c$)$ What would be the displacement vector for the portion of the path going from flower $1$ to flower $\backslash (2\backslash$left$(\backslash$Delta $\backslash$mathbf$\{$x$\}\_\{1\backslash$rightarrow $2\}\backslash$right$)\backslash )?$ Hint: Remember that the displacement is the final position minus the initial position of an object.

$($d$)$ What would be the total distance $\backslash ($ d $\backslash )$ covered by the bee as it moves along this path $($from hive, to flower $1,$ to flower $2,$ and to flower $3)?$ If you have trouble answering this one, explain how you would calculate the distance using your plot from part $($a$).$