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Math Help - cross product(vectors)

  1. #1
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    cross product(vectors)

    express the vector V as the sum of a vector parallel to B and a vector orthagonal to B
    V=4i-2j+6k, B=-2i+j-3k

    I got the orthognal as 7/3(-2i+j-3k)
    but i dont understand the first part for the line of me!please help someone
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  2. #2
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    Quote Originally Posted by Country_boy_88 View Post
    express the vector V as the sum of a vector parallel to B and a vector orthagonal to B
    V=4i-2j+6k, B=-2i+j-3k

    I got the orthognal as 7/3(-2i+j-3k)
    but i dont understand the first part for the line of me!please help someone
    1.You may have noticed that \vec V = (-2) \cdot \vec B . That means \vec V and \vec B are collinear (or in simple terms: They are parallel).

    2. Let \vec N denote the vector orthogonal to \vec B (by the way there are an unlimited number of such vectors!) then you have to determine \vec N:

    \vec V = (k) \cdot \vec B + \vec N with k \in \mathbb{R}

    You'll get \vec N = \vec 0 where \vec 0 is the nullvector. (Per definition the nullvector is orthogonal to every vector)
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