The two vectors (say A and B) of different magnitudes cannot be combined to give zero resultant since minimum value of combination is ІA-BІ which is not zero if AB.
The three vectors A, B and C of 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...
Materials show varying behaviors based on their Poisson's ratio. High Poisson's ratio materials (near 0.5) contract significantly sideways when stretched and expand when compressed, seen in substances like rubber. Low Poisson's ratio materials (near 0) undergo minimal width change during axial deformation, typical of metals and common engineering materials.
If a vector A is multiplied by a real number (say n), the vector of same nature is obtained but its magnitude is n times that of A.
