Is it true that $left(vec w-dfrac12vec uright)perpleft(2vec w-vec uright);forallvec u,vec w$?

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True or false? Let $vec u$ and $vec w$ two vectors. Then $vec w-dfrac12vec u$ and $2vec w-vec u$ are perpendicular.



I think is false. Let $vec u=(1,0,0)$ and $vec w=(0,1,0)$ two vectors. Then $$left(vec w-dfrac12vec uright)cdotleft(2vec w-vec uright)=left(-dfrac 12,1,0right)cdotleft(-1,2,0right)=dfrac12+2=dfrac52neq0.$$



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linear-algebra vectors




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    Yes, you are correct.
    – saulspatz
    Aug 17 at 2:37














up vote
2
down vote

favorite












True or false? Let $vec u$ and $vec w$ two vectors. Then $vec w-dfrac12vec u$ and $2vec w-vec u$ are perpendicular.



I think is false. Let $vec u=(1,0,0)$ and $vec w=(0,1,0)$ two vectors. Then $$left(vec w-dfrac12vec uright)cdotleft(2vec w-vec uright)=left(-dfrac 12,1,0right)cdotleft(-1,2,0right)=dfrac12+2=dfrac52neq0.$$



Is it correct?



Thanks!




linear-algebra vectors




share|cite|improve this question
















  • 1




    Yes, you are correct.
    – saulspatz
    Aug 17 at 2:37












up vote
2
down vote

favorite









up vote
2
down vote

favorite











True or false? Let $vec u$ and $vec w$ two vectors. Then $vec w-dfrac12vec u$ and $2vec w-vec u$ are perpendicular.



I think is false. Let $vec u=(1,0,0)$ and $vec w=(0,1,0)$ two vectors. Then $$left(vec w-dfrac12vec uright)cdotleft(2vec w-vec uright)=left(-dfrac 12,1,0right)cdotleft(-1,2,0right)=dfrac12+2=dfrac52neq0.$$



Is it correct?



Thanks!




linear-algebra vectors




share|cite|improve this question












True or false? Let $vec u$ and $vec w$ two vectors. Then $vec w-dfrac12vec u$ and $2vec w-vec u$ are perpendicular.



I think is false. Let $vec u=(1,0,0)$ and $vec w=(0,1,0)$ two vectors. Then $$left(vec w-dfrac12vec uright)cdotleft(2vec w-vec uright)=left(-dfrac 12,1,0right)cdotleft(-1,2,0right)=dfrac12+2=dfrac52neq0.$$



Is it correct?



Thanks!





linear-algebra vectors





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share|cite|improve this question




share|cite|improve this question










asked Aug 17 at 2:32









manooooh

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  • 1




    Yes, you are correct.
    – saulspatz
    Aug 17 at 2:37












  • 1




    Yes, you are correct.
    – saulspatz
    Aug 17 at 2:37







1




1




Yes, you are correct.
– saulspatz
Aug 17 at 2:37




Yes, you are correct.
– saulspatz
Aug 17 at 2:37










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They are parallel
$$left(2vec w-vec uright)=2left(vec w-dfrac12vec uright)$$
this shows one is a factor of the another.






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    1 Answer
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    up vote
    3
    down vote



    accepted










    They are parallel
    $$left(2vec w-vec uright)=2left(vec w-dfrac12vec uright)$$
    this shows one is a factor of the another.






    share|cite|improve this answer
























      up vote
      3
      down vote



      accepted










      They are parallel
      $$left(2vec w-vec uright)=2left(vec w-dfrac12vec uright)$$
      this shows one is a factor of the another.






      share|cite|improve this answer






















        up vote
        3
        down vote



        accepted







        up vote
        3
        down vote



        accepted






        They are parallel
        $$left(2vec w-vec uright)=2left(vec w-dfrac12vec uright)$$
        this shows one is a factor of the another.






        share|cite|improve this answer












        They are parallel
        $$left(2vec w-vec uright)=2left(vec w-dfrac12vec uright)$$
        this shows one is a factor of the another.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Aug 17 at 2:42









        Nosrati

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