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Math Help - Decomposing vectors.

  1. #1
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    Decomposing vectors.

    Take n = 2i + j - k as a normal vector of the plane p. Decompose the vector QO into the sum of two vectors; one of them is parallel to n and the other one is orthogonal to n.
    So far I got, Q(0,0,-1) and (0,0,0) for the origin. and QO = (0,0,1).
    n=2i+j-k
    o=ai+bj+ck
    (2+a)i+(1+b)j+(-1+c)k=0i+0j+k
    I get a=-2, b=-1, c=2. Therefore o = -2i-j+2k
    But the dot product of these two vectors is not equal to zero so the equation for o is incorrect. When i test i-j+k the dot product is zero but how would I know for sure without trial and error.
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    Re: Decomposing vectors.

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