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Math Help - Find a Vector given a length

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    Super Member craig's Avatar
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    Find a Vector given a length

    Hi, it's been a while since I've attempted anything to do with vectors and I'm a little rusty at the moment.

    The question is:

    Fine a vector length 2\sqrt{6} anti-parallel to d = (-1,2,-1).

    I thought that maybe the vector product would be the way forward but no idea where to start.

    Any help would be greatly appreciated.

    Thanks

    Craig
    Last edited by craig; October 19th 2009 at 02:43 PM.
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    Quote Originally Posted by craig View Post
    Hi, it's been a while since I've attempted anything to do with vectors and I'm a little rusty at the moment.

    The question is:

    Fine a vector length 2\sqrt{6} anti-parallel to [tex]d = (-1,2,-1)[/MATH.

    I thought that maybe the vector product would be the way forward but no idea where to start.

    Any help would be greatly appreciated.

    Thanks

    Craig


    What about 2\left(1,-2,1\right)=\left(2,-4,2\right) ?

    Tonio
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    Super Member craig's Avatar
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    Quote Originally Posted by tonio View Post
    What about 2\left(1,-2,1\right)=\left(2,-4,2\right) ?

    Tonio
    Hi Tonio thank's for the reply.

    How did you come up with this answer?
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    Quote Originally Posted by craig View Post
    Hi Tonio thank's for the reply.

    How did you come up with this answer?

    Antiparallel ==> it has to "go the other way" so multiply by -1 all its entries.
    Now, the vector given and the new one both have norm =\sqrt{6} so in order to get norm equal to 2\sqrt{6} simply multiply the vector by 2.

    Tonio
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    Quote Originally Posted by craig View Post
    Hi, it's been a while since I've attempted anything to do with vectors and I'm a little rusty at the moment.

    The question is:

    Fine a vector length 2\sqrt{6} anti-parallel to d = (-1,2,-1).

    I thought that maybe the vector product would be the way forward but no idea where to start.

    Any help would be greatly appreciated.

    Thanks

    Craig
    Any vector parallel to (-1, 2, -1) must be of the form a(-1, 2, -1)= (-a, 2a, -a). Any vector anti-parallel to (-1, 2, -1) (in the opposite direction) must be of that form with a negative- or we can write it -a(-1, 2, -1)= (a, -2a, a) with the requirement that a be positive.

    Now, the length of (a, -2a, a) is \sqrt{a^2+ (-2a)^2+ a^2}= \sqrt{6a^2}= a\sqrt{6}. In order that the vector have length 2\sqrt{6}, we must have a\sqrt{6}= 2\sqrt{6} or a= 2. (a, -2a, a)= (2, -4, 2).
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    Super Member craig's Avatar
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    Thanks for both replys, all makes sense now. It's been a very long time since I've attempted anything to do with vectors, got quite a bit of catching up to do
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