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Math Help - Determine if two vectors are orthogonal

  1. #1
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    Determine if two vectors are orthogonal

    Hey everyone! I have a question about the orthogonality of two vectors

    The question is: It is given: llmll = 4; llnll = square root of 3; (m^,n)= 150 degrees

    (i) find the norm of the vector m + 2n
    (ii) Determine if the vectors (m+2n) and (-m+n) are orthogonal

    I got an answer of 2 for the norm but I don't know what to do for the second part. Do I just substitute the values of m and n into the vectors and if they both equal 0 when multiplied, they are orthogonal? Any help would be greatly appreciated
    Last edited by hemster83; September 26th 2012 at 03:10 PM.
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    Re: Determine if two vectors are orthogonal

    Quote Originally Posted by hemster83 View Post
    Hey everyone! I have a question about the orthogonality of two vectors

    The question is: It is given: llmll = 4; llnll = square root of 3; (m^,n)= 150 degrees

    (i) find the norm of the vector m + 2n
    (ii) Determine if the vectors (m+2n) and (-m+n) are orthogonal
    What does the notation (m^,n)= 150 degrees mean?
    I have never seem that used.
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  3. #3
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    Re: Determine if two vectors are orthogonal

    Quote Originally Posted by Plato View Post
    What does the notation (m^,n)= 150 degrees mean?
    I have never seem that used.
    It means the angle between m and n equals 150 degrees. I think my prof made it up himself
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    Re: Determine if two vectors are orthogonal

    Quote Originally Posted by hemster83 View Post
    It means the angle between m and n equals 150 degrees. I think my prof made it up himself
    How very odd is that?


    Quote Originally Posted by hemster83 View Post
    The question is: It is given: llmll = 4; llnll = square root of 3; (m^,n)= 150 degrees
    (i) find the norm of the vector m + 2n
    (ii) Determine if the vectors (m+2n) and (-m+n) are orthogonal
    Well you know that \frac{{m \cdot n}}{{\left\| m \right\|\left\| n \right\|}} = \cos \left( {\frac{{5\pi }}{6}} \right) = \frac{{ - \sqrt 3 }}{2}.

    From that you can find m\cdot n~.

    Now \|m+2n\|^2=(m+2n)\cdot(m+2n)=m\cdot m+4(n\cdot m)+4(n\cdot n)~.
    Last edited by Plato; September 26th 2012 at 03:58 PM.
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    Re: Determine if two vectors are orthogonal

    I have this same exact question.


    Well you know that \frac{{m \cdot n}}{{\left\| m \right\|\left\| n \right\|}} = \cos \left( {\frac{{5\pi }}{6}} \right) = \frac{{ - \sqrt 3 }}{2}.

    From that you can find m\cdot n~.

    Now \|m+2n\|^2=(m+2n)\cdot(m+2n)=m\cdot m+4(n\cdot m)+4(n\cdot n)~.
    Now this is the method I used to find the norm, or length of the vector (m+2n). However, I am still at a loss as to how to test the orthogonality of the two vectors (m+2n) and (-m+n).

    Thanks in advance.
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    Re: Determine if two vectors are orthogonal

    Quote Originally Posted by Kristoffermk3 View Post
    I have this same exact question.
    Now this is the method I used to find the norm, or length of the vector (m+2n). However, I am still at a loss as to how to test the orthogonality of the two vectors (m+2n) and (-m+n).

    What is (m+2n)\cdot(-m+n)=~?
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  7. #7
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    Re: Determine if two vectors are orthogonal

    Yes, that's what i'm looking for.

    I suppose the part that is confusing me is simply that its not asking something as simple as (m dot n). Which is very simple to figure out, but I am confused on how to approach this when they are combinations of vectors such as (m+2n) and (-m+n)...
    Last edited by Kristoffermk3; January 25th 2013 at 02:55 PM.
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    Re: Determine if two vectors are orthogonal

    Quote Originally Posted by Kristoffermk3 View Post
    Yes, that's what i'm looking for.

    I suppose the part that is confusing me is simply that its not asking something as simple as (m dot n). Which is very simple to figure out, but I am confused on how to approach this when they are combinations of vectors such as (m+2n) and (-m+n)...

    (m+2n)\cdot(-m+n)=-m\cdot m-2 m\cdot n+m\cdot n+2n\cdot n
    Thanks from Kristoffermk3
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  9. #9
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    Re: Determine if two vectors are orthogonal

    Oh my, that seems so self-evident now.

    Thank you very much for your clarification.
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