Question

17) A particle moves on a given straight line with a constant
speed v. At a certain time it is at a point P on its straight
line path. O is a fixed point. Show that OP xv is
independent of the position P. exp with figure​

Answer 1

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