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Math Help - Orthogonal Vectors

  1. #1
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    Orthogonal Vectors

    Let u = <-1, 1, 2> and v = <2, -1, -1>. Find all unit vectors orthogonal to both u and v.

    I know that one can use cross products to find a vector orthgonal to both u and v and scale it down to be a unit vector. But the question says to find all the unit vectors and I don't know how to go about doing that since there is an infinite number of them.
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  2. #2
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    It is really simple:  \pm \frac{{u \times v}}{{\left\| {u \times v} \right\|}}.
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  3. #3
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    So, the answer would be + or -(i + 3j - k)/(sqrt 11) ? Or would I go ahead and say it's <(1/(sqrt 11)), (3/(sqrt 11)), (-1)/(sqrt11)> But isn't that just one unit vector orthogonal to u and v, not all of them?
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  4. #4
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    Quote Originally Posted by kiddopop View Post
    But isn't that just one unit vector orthogonal to u and v, not all of them?
    What do you think \pm means?
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  5. #5
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    Oh. Yeah. I forgot about that in front. My bad.
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