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A particle moves along a line with a con...

A particle moves along a line with a constant speed v. At a certain time it is at a point P on its straight line path, O is fixed point. Prove that `(vecOPxxvecv)` is independent of the position P.

Text Solution

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Let `vec(v)=v hat(i)` & `vec(OP)=xhat(i)+yhat(j)=xhat(i)+dhat(j)`

so `vec(OP)xxvec(v)=(xhat(i)+dhat(j))xxvhat(i)=-dvhat(k)`
(d= is constant)
which is independent of position.
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