Consult Multiple Concept Example $9$ in preparation for this problem. A golfer, putting on a green, requires three strokes to "hole the ball." During the first putt, the ball rolls $3\mathrm{.}2$ m due east. For the second putt, the ball travels $1\mathrm{.}3$ m at an angle of $20\mathrm{.}0\backslash$deg north of east. The third putt is $0\mathrm{.}53$ m due north. What displacement $(($a$)$ magnitude and $($b$)$ direction relative to due east$)$ would have been needed to $$hole the ball$$ on the very first putt?