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Math Help - Vectors!!

  1. #1
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    Vectors!!

    Hey guys,

    This problem about vectors is giving me some trouble. Help would be greatly appreciated.

    Let v= <2,3,2> and w= <4,6,5>

    a) Find a unit vector that is orthogonal to both v and w.

    b) Find the angle formed by vectors v x w and w x v

    c) If u= <-1,4,8> find the cosine of the angle formed by vectors u and v x w

    Thanks so much!!
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  2. #2
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    Re: Vectors!!

    Quote Originally Posted by blackflag10 View Post
    Let v= <2,3,2> and w= <4,6,5>
    a) Find a unit vector that is orthogonal to both v and w.

    b) Find the angle formed by vectors v x w and w x v

    c) If u= <-1,4,8> find the cosine of the angle formed by vectors u and v x w
    For a) find \frac{v\times w}{\|v\times w\|}.

    For b) here is a hint: v\times w= -w\times v.

    c) \frac{u\cdot(v\times w)}{\|u\|\|v\times w\|}
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  3. #3
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    Re: Vectors!!

    Quote Originally Posted by Plato View Post
    For a) find \frac{v\times w}{\|v\times w\|}.

    For b) here is a hint: v\times w= -w\times v.

    c) \frac{u\cdot(v\times w)}{\|u\|\|v\times w\|}
    OK, I got A and C. I don't know how I did not see that the first time. But for B, would it be 180 degrees? Would they form a straight line?

    Thank you so much!
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  4. #4
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    Re: Vectors!!

    Quote Originally Posted by blackflag10 View Post
    for B, would it be 180 degrees? Would they form a straight line?
    That is correct.
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  5. #5
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    Re: Vectors!!

    Thanks!!
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  6. #6
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    Re: Vectors!!

    Another useful formula when you have two vectors a dot b = |a||b| cos theta
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