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Math Help - Perpendicular Vectors

  1. #1
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    Perpendicular Vectors

    Hi again

    I am looking for a unit vector that is perpendicular to the following vectors

    a= 3i-j+4k
    b=-3i-2j+2k

    So I know that find a perpendicular vector that a.b=0

    So I get (3,-1,4).(-3,-2,2)= (-9,2,8) but this isn't one of the options. I know that multiples of it can be also perpendicular, can someone point out where I'm going wrong?

    Thanks
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  2. #2
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    OK... I have seen an error in what I'm doing here. I want a vector perpendicular to both of them - they aren't perpendicular to each other so I can't find the dot product of a and b.

    So what would I do instead? I'm very confused
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  3. #3
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    Hello,
    Quote Originally Posted by Ian1779 View Post
    OK... I have seen an error in what I'm doing here. I want a vector perpendicular to both of them - they aren't perpendicular to each other so I can't find the dot product of a and b.

    So what would I do instead? I'm very confused
    Do you know about the cross product ? (Cross product - Wikipedia, the free encyclopedia)

    There's the formula in this section The explanation of what the cross product is is above.

    And if you want a unit vector, once you get the result of the cross product, divide each ordinate by the length of the vector, that is \sqrt{x^2+y^2+z^2} for a vector (x,y,z)
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  4. #4
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    I did know about the cross product, but didn't realise I had to use it in this context.

    I've now got the cross product which is 6i+18j-9k

    So I am dividing this now by \sqrt{6^2+18^2+(-9)^2} Is that right? If so I think I'm there giving me

    {\frac{2}{7}}i+{\frac{6}{7}}j-{\frac{3}{7}}k

    I hope I've got it?!
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  5. #5
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    You missed a sign in the cross product: 6i-18j-9k
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  6. #6
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    Quote Originally Posted by Ian1779 View Post
    I did know about the cross product, but didn't realise I had to use it in this context.

    I've now got the cross product which is 6i-18j-9k

    So I am dividing this now by \sqrt{6^2+18^2+(-9)^2} Is that right? If so I think I'm there giving me

    {\frac{2}{7}}i-{\frac{6}{7}}j-{\frac{3}{7}}k

    I hope I've got it?!
    You can check by doing the scalar product with each of the other vectors =)
    You can also check whether or not it is a unit vector, by calculating the norm of the latter vector.
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