Answer
The resultant vector with the smallest magnitude is $F_{1}+F_{3}=10.0N$, due east,
and the one with the largest magnitude is $F_{3}+F_{4}=70.0N$, due west.
Work Step by Step
Six possible combinations for the two vectors will lead to the following resultant vectors:
$F_{1}+F_{2}=50.0N+10.0N=+60.0N=60N$, due east
$F_{1}+F_{3}=50.0N-40.0N=+10.0N=10.0N$, due east
$F_{1}+F_{4}=50.0N-30.0N=+20.0N=20.0N$, due east
$F_{2}+F_{3}=10.0N-40.0N=-30.0N=30.0N$, due west
$F_{2}+F_{4}=10.0N-30.0N=-20.0N=20.0N$, due west
$F_{3}+F_{4}=-40.0N-30.0N=-70.0N=70.0N$, due west
The resultant vector with the smallest magnitude is $F_{1}+F_{3}=10.0N$, due east,
and the one with the largest magnitude is $F_{3}+F_{4}=70.0N$, due west.
