using capitals for vector notation.if A and B are two nonzero vectors and dA/dt=BXA(cross product), then which one is correct- a)dA/dt=0 b)dB/dt=0 c)d|A|/dt=0 d)d|B|/dt=0.plz explain the reason.

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).

Approved