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Math Help - Vector projection

  1. #1
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    Vector projection

    u= (((3i + j) dotted with (i + j)) * (i +j)) / (|i = j|^2). I tried to simplify to
    u = (3i + j)*(i + j) / (i^2 +j^2) and from here i don't know how to simplify further. Apparently it is simplified to 4/2 (i + j) = 2i + 2j.
    The initial question states, express the vector 3i + j as a su of vectors u + v, where u is parallel to vector i + j and v is perpendicular to u. I am interested in the vector projection solution.

    Help would be nice!
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  2. #2
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    Quote Originally Posted by Zamzen View Post
    express the vector 3i + j as a sum of vectors u + v, where u is parallel to vector i + j and v is perpendicular to u. I am interested in the vector projection solution.
    Your post is very difficult to read.
    So I will answer the question quoted above.

    Suppose that \vec{a}~\&~\vec{b} are vectors.
    We can write  \vec{a} as the sum  \vec{a} =\vec{b}_{||} +\vec{b}_{\|} where  \vec{b}_{\|} is parallel to  \vec{b} and  \vec{b}_{\bot} is perpendicular to  \vec{b}.

     \vec{b}_{\|}=\dfrac{\vec{a}\cdot\vec{b}}{\vec{b}\c  dot\vec{b}}~\vec{b}

     \vec{b}_{\bot}= \vec{a} -\vec{b}_{\|}
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