1. A particle moves on a given straight line with a constant speed v. at a certain time it is at point P on its straight line path. O is a fixed point. Show that vectorOP × vectorv is independent of the position P.
1. A particle moves on a given straight line with a constant speed v. at a certain time it is at point P on its straight line path. O is a fixed point. Show that vectorOP × vectorv is independent of the position P.
Every point on the path of the particle may be written:
,
where is the position of the particle at .
Then:
which is independent of , and so of the particular point .