A particle moves on a given straight line with a constant speed v. At a certain time it is at a point P o its straight lline path.O is a fixed point. Show than `vec(OP)xxvec upsilon` is independent of the position P.?

Explanation

The particle moves on the straight line `P_1` t speed v from the figure
`vec(OP)xxv=(OP)v sin hat n, v (OP) sin theta hatn
=v(OQ)hat n`
It can be seen from theure, `OQ=OP=sin theta, =OP_1 sin theta`So, whatever may be the position of the particle the magnitude and direction of `vec(OP)xxvecv` remain constant
`vec(OP)xxvecv` is independent of the position P.