Which two vectors add together to give a resultant with the smallest magnitude, and which two vectors add to give a resultant with the largest magnitude? in each case specify the magnitude and direction of the resultant?

Two vectors in the opposite direction of each other gives the smallest resultant, where as two vector in the same direction gives the largest resultant.

Smallest Resultant: when two vectors, acts in opposite direction (180°) to each other, the resultant of these vector is simply the subtraction of both the vectors, having the direction of largest magnitude vector.

Largest resultant: when two vectors, acts in same direction (0°) to each other, the resultant of these vector is simply the addition of both the vectors, having the same direction as the forming vectors.

it is the second option.

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)