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Math Help - Vectors

  1. #1
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    Vectors

    Relative to a fixed origin, O, the line l has the equation:

    r = (\b i + 7\b j - 5 \b k) + \lambda(3 \b i - \b j + 2 \b k)

    The point C lies on l and is such that OC is perpendicular to l.

    EDIT: The question is - Find the coordinates of C.
    Last edited by Simplicity; June 7th 2008 at 11:46 AM.
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  2. #2
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    you forgot to post a question.

    also this problem looks similar to the this one

    Bobak
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  3. #3
    o_O
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    Let this point be C(a,b,c) and \vec{OC} = (a,b,c)

    Since C is on the line, we can see that: a = 1 + 3\lambda, b = 7 - \lambda, c = -5 + 2\lambda

    Since \vec{OC} \perp (3, -1, 2) , then \vec{OC} \cdot (-3,-1,2) = 0:

    -3a - b + 2c = 0

    Convert a,b, c into terms of lambda and solve for it. Then, plug it in back to the equation of your line to get \vec{r} which should correspond to your point as it originates form the origin.
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    Quote Originally Posted by bobak View Post
    you forgot to post a question.

    also this problem looks similar to the this one

    Bobak
    Ooop, here it is...

    'Find the coordinates of C.'
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  5. #5
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    Quote Originally Posted by o_O View Post
    Let this point be C(a,b,c) and \vec{OC} = (a,b,c)

    Since C is on the line, we can see that: a = 1 + 3\lambda, b = 7 - \lambda, c = -5 + 2\lambda

    Since \vec{OC} \perp (3, -1, 2) , then \vec{OC} \cdot (-3,-1,2) = 0:

    -3a - b + 2c = 0

    Convert a,b, c into terms of lambda and solve for it. Then, plug it in back to the equation of your line to get \vec{r} which should correspond to your point as it originates form the origin.
    So, if it is perpendicular it is equated to zero. What about if it was parallel?
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  6. #6
    Moo
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    Hello,

    Quote Originally Posted by Air View Post
    So, if it is perpendicular it is equated to zero. What about if it was parallel?
    The two vectors would be proportional (with a common ratio), because they have the same direction
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