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Question

Two vectors have magnitudes V1 = 2.0 km and V2 = 4.5 km. What are the maximum and minimum magnitudes of their vector sum?
Maximum

Minimum

Answer 1

Maximum:
The magnitude of the vector sum of two vectors is a maximum when their directions are acting directly in support of each other (their angular difference is 0 degrees). In this case, the magnitude of the vector sum is the algebraic sum of the individual vector magnitudes.

s = V1 + V2
s = 2 + 4.5
s = 6.5 km

note: the direction of the vector sum is the same as the direction of the two individual vectors (that points to the same direction).


Minimum:
The magnitude of the vector sum of two vectors is a minimum when their directions are acting in direct opposition with each other (their angular difference is 180 degrees). In this case, the magnitude of the vector sum is the algebraic difference of the individual vector magnitudes.

s = V2 - V1
s = 4.5 - 2
s = 2.5 km

note: the direction of the vector sum follows the direction of the vector with the greater magnitude. The vector sum is 2.5 km and its direction is the same as the direction of vector V2 (the greater of the two vectors).

Answer 2

These are not vectors
Vector must have not only a magnitude but also a direction.