If vectors are arranged as trigonal planar and have equal magnitude, it is an ideal case of zero resultant.

The two vectors (say A and B) of different magnitudes cannot be combined togive zero resultant since minimum value of combination isІA-BІ which is not zero if AB.

The three vectors A, B and Cof different magnitudes can be zero such that they form a closed triangle, then,

A+B+C=0

or, C=-(A+B)

Hence, the sum of three vectors may be zero if vector sum of any two vectors is equal and opposite to the third vector.

Note: The vectors can give this result only if they lie in the same plane. If three...

Yes, a physical quantity can have magnitude and direction but still be a scalar if it doesn't obey the vector addition. An example is Electric Current which has magnitude and a fixed direction, but it does not follow vector laws of addition.

Let the forces be F1 and F2 at an angle A and their resultant be F. According to question,

| F1 | = | F2 | = | F |

We know,

F^2 = F1^2 + F2^2 + 2 F1 F2 cos A

or, F^2 = F^2 + F^2 + 2 F F cos A

or, F^2 - 2F^2 = 2 F^2 cos A

or, - F^2 = 2 F^2 cos A

or, -1 = 2 cos A

or, cos A = -1/2

or, cos A = cos 120

So, A = 120 degrees.

Hence, when two forces of equal magnitude act at an angle of 120 degrees, the resultant is equal to one of the forces.