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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.

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.

Grade:12

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

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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