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Math Help - please help with vectors

  1. #1
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    please help with vectors

    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.
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  2. #2
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    Quote Originally Posted by vritikagupta View Post
    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:

    \bold{p}=\bold{p_0}+\bold{v}t,

    where \bold{p_0} is the position of the particle at t=0.

    Then:

    \bold{p}\wedge \bold{v}= (\bold{p_0}+\bold{v}t) \wedge \bold{v}<br />
=\bold{p_0}\wedge \bold{v}+(\bold{v} \wedge \bold{v})t=\bold{p_0}\wedge \bold{v}<br />

    which is independent of t, and so of the particular point \bold{p}.

    RonL
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