Please clarify what "base" you are talking about.
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Undefined: You cannot divide by zero
No. You cannot divide by zero.
The denominator of any number cannot be zero because division by zero is not defined.
The only way that two vectors add up to zero is if they have equal magnitude and opposite direction. If the magnitudes are not equal then no, they cannot give a zero resultant.
That's close to the definition of a rational number.