About is tangent vector?

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Vector equation for a line is like this $$r(t)=r_0+tv$$



But I wonder, when $tv$ is like $$langle t,frac-3t4,frac3t2rangle$$ then can I make it look better like $$langle4t, -3t, 6trangle$$







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    Vector equation for a line is like this $$r(t)=r_0+tv$$



    But I wonder, when $tv$ is like $$langle t,frac-3t4,frac3t2rangle$$ then can I make it look better like $$langle4t, -3t, 6trangle$$







    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Vector equation for a line is like this $$r(t)=r_0+tv$$



      But I wonder, when $tv$ is like $$langle t,frac-3t4,frac3t2rangle$$ then can I make it look better like $$langle4t, -3t, 6trangle$$







      share|cite|improve this question














      Vector equation for a line is like this $$r(t)=r_0+tv$$



      But I wonder, when $tv$ is like $$langle t,frac-3t4,frac3t2rangle$$ then can I make it look better like $$langle4t, -3t, 6trangle$$









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      share|cite|improve this question




      share|cite|improve this question








      edited Aug 29 at 8:54









      gimusi

      71.2k73786




      71.2k73786










      asked Aug 29 at 8:52









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          Yes of course any non zero multiple of $v=left(1,frac-34,frac32right)$ can be used as direction vector for the given line.



          Indeed just assume a scaling factor for the parameter as for example $t=4bar t$ to obtain



          $$tv=4bar t v=bar t (4v)$$



          and the two lines with $t,bar t in mathbbR$



          • $r(t)=r_0+tv$

          • $bar r(t)=r_0+bar t(4v)$

          decribe, with different parametrization, the same set of points in $mathbbR^3$.






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            1 Answer
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            1 Answer
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            up vote
            0
            down vote













            Yes of course any non zero multiple of $v=left(1,frac-34,frac32right)$ can be used as direction vector for the given line.



            Indeed just assume a scaling factor for the parameter as for example $t=4bar t$ to obtain



            $$tv=4bar t v=bar t (4v)$$



            and the two lines with $t,bar t in mathbbR$



            • $r(t)=r_0+tv$

            • $bar r(t)=r_0+bar t(4v)$

            decribe, with different parametrization, the same set of points in $mathbbR^3$.






            share|cite|improve this answer


























              up vote
              0
              down vote













              Yes of course any non zero multiple of $v=left(1,frac-34,frac32right)$ can be used as direction vector for the given line.



              Indeed just assume a scaling factor for the parameter as for example $t=4bar t$ to obtain



              $$tv=4bar t v=bar t (4v)$$



              and the two lines with $t,bar t in mathbbR$



              • $r(t)=r_0+tv$

              • $bar r(t)=r_0+bar t(4v)$

              decribe, with different parametrization, the same set of points in $mathbbR^3$.






              share|cite|improve this answer
























                up vote
                0
                down vote










                up vote
                0
                down vote









                Yes of course any non zero multiple of $v=left(1,frac-34,frac32right)$ can be used as direction vector for the given line.



                Indeed just assume a scaling factor for the parameter as for example $t=4bar t$ to obtain



                $$tv=4bar t v=bar t (4v)$$



                and the two lines with $t,bar t in mathbbR$



                • $r(t)=r_0+tv$

                • $bar r(t)=r_0+bar t(4v)$

                decribe, with different parametrization, the same set of points in $mathbbR^3$.






                share|cite|improve this answer














                Yes of course any non zero multiple of $v=left(1,frac-34,frac32right)$ can be used as direction vector for the given line.



                Indeed just assume a scaling factor for the parameter as for example $t=4bar t$ to obtain



                $$tv=4bar t v=bar t (4v)$$



                and the two lines with $t,bar t in mathbbR$



                • $r(t)=r_0+tv$

                • $bar r(t)=r_0+bar t(4v)$

                decribe, with different parametrization, the same set of points in $mathbbR^3$.







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited Aug 29 at 9:03

























                answered Aug 29 at 8:53









                gimusi

                71.2k73786




                71.2k73786



























                     

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