Two forces 12N and 16N are acting upon a body. What can be the maximum and minimum resultant force on the body?

Hello!

Let's assume that both forces are apllied to the same point. In another case they would cause rotation of a body and it would be unclear what the net force is.

Forces are vectors. Two vectors a and b with the same starting point are always lie in the same two dimensional plane. The magnitude of their sum is the square root of the dot product:

where c is the angle between a and b.

The maximum value of this magnitude is reached when cos(c) = 1, this means the vectors have the same direction. The value is actually |a| + |b| = 12 N + 16 N = 28 N.

The minimum is reached when cos(c) = -1, when the vectors have opposite directions. And this minimum value is ||a| - |b|| = 16 N - 12 N = 4 N.