Question

a particle moves on a straight line at constant speed v. At certain time it is at point p on straight line path. o is a fixed point. show that op vector × v vector is independent of position p.

Answer 1

ANSWER::

For better understanding see the figure.

The particle moves on the straight line PP' at speed v.

According to the figure,

OP x v = (OP) v sinФ n = v(OP) sinФ n = v(OQ) n

So, we can see that from the figure,

OQ = OP sin Ф = OP' sin Ф'

So, the magnitude of OP x v remain constant irrespective of the position of the particle.

Therefore , OP x v is independent of position P.

Hope it helps!