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Hi Ashmita,
For cross product of X,Y to be defined, both X and Y must be vectors.
So d|A|/dt = Ax|A|, has no meaning. (Because |A| is a scalar)
Similarly d|B|/dt has no meaning.
Now dA/dt = BxA (angle between A and B can be anything, so BxA need not necessarily be zero)
But consider dB/dt = BxB (angle between the same vectors, which would be parallel, would be zero)
So BxB = (|B|)(|B|)sin(0) {The magnitude is zero}.
Hence Option (B).
All the best.
Regards,
Ashwin (IIT Madras).
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