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    Im finding some vectors quite challenging. Im not sure how i find the point on a vector line which is closest to the origin.

    I know what it is perpendular to the orogin. So the vector product equals zero. However i end up forming quadratics which dont lead anywhere.

    How should i approach these kinds of questions.

    I am given the vector line equation and a point on the line. I am told to find the clostest point to the origin.

    Thanks.
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    (Original post by jamesgates1)
    Im finding some vectors quite challenging. Im not sure how i find the point on a vector line which is closest to the origin.

    I know what it is perpendular to the orogin. So the vector product equals zero. However i end up forming quadratics which dont lead anywhere.

    How should i approach these kinds of questions.

    I am given the vector line equation and a point on the line. I am told to find the clostest point to the origin.

    Thanks.
    Well, you know the parametric equation of a point on the plane is (all the english letters are going to be given):

    x = a + \lambda b
    y = c + \lambda d
    z = e + \lambda f

    Call this general point X

    Then you know \vec{OX}. Now you need to find \lambda s.t \vec{OX} \cdot \ell = 0 where \ell is the direction vector of the line (all this says is make the line OX perpendicuar to your vector line). This gives you a (linear) equation solely in \lambda which you can then solve for and then plug this into \vec{OX} after which, you then calculate the magnitude of \vec{OX}.

    I had to make this all very abstract with so many variables because you didn't give me an example to work off, sorry!
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    (Original post by Zacken)
    Well, you know the parametric equation of a point on the plane is (all the english letters are going to be given):

    x = a + \lambda b
    y = c + \lambda d
    z = e + \lambda f

    Call this general point X

    Then you know \vec{OX}. Now you need to find \lambda s.t \vec{OX} \cdot \ell = 0 where \ell is the direction vector of the line (all this says is make the line OX perpendicuar to your vector line). This gives you a (linear) equation solely in \lambda which you can then solve for and then plug this into \vec{OX} after which, you then calculate the magnitude of \vec{OX}.

    I had to make this all very abstract with so many variables because you didn't give me an example to work off, sorry!
    Thanks. I understand it now!
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    (Original post by jamesgates1)
    Thanks. I understand it now!
    No problem, make sure to test it out on a few problems but it's usually a method that has served me very well.
 
 
 
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