The minimum number of vectors having different planes which can be added to give zero resultant is
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If the vectors are in different planes, they would need to cancel components in at least 3 dimensions to make the resultant 0.
Hence, we would need at least 4 vectors such that 3 of them when added cancel their components in a plane and add to get a single vector perpendicular to this plane. Fourth vector would nullify this perpendicular vector.
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