Yes, a vector which has zero magnitude is also a vector in case of two vectors travelling in opposite directions with equal magnitudes. At this case, the resultant vector has zero magnitude but it is still a vector. We call it a null vector.
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No, if three vectors do not lie in a plane, they cannot give zero resultant.
Explanation:
Let A, B and C be three vectors. If they give zero resultant, then
A+B+C=0
or, A= -(B+C)
Hence, they will produce zero resultant, if A is equal to negative of vector (B+C). The vector (B+C) lies in the plane of B and C. Hence, A will be equal to negative of (B+C) if A, B and C all lie in a plane.
