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Math Help - Gr 12. Vector Question Involving Dot Product of Two Vectors(Part 2)

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    Gr 12. Vector Question Involving Dot Product of Two Vectors(Part 2)

    I don't know if I'm being abusive posting another thread so let me know if there is a limit on how much question/threads I can post a day in this forum or any other thanks! But I got another tricky question, much more trickier!

    Find a unit vector that is parallel to the xy-plane and perpendicular to the vector 4i - 3j + k (4, -3, 1)

    So how would I go about doing this questions? Thanks
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    Quote Originally Posted by narutoblaze View Post
    I don't know if I'm being abusive posting another thread so let me know if there is a limit on how much question/threads I can post a day in this forum or any other thanks! But I got another tricky question, much more trickier!

    Find a unit vector that is parallel to the xy-plane and perpendicular to the vector 4i - 3j + k (4, -3, 1)

    So how would I go about doing this questions? Thanks
    Let the sought vector be \textbf u=a\,\textbf i+b\,\textbf j+c\,\textbf k\text. The two vectors must be orthogonal, so

    4a-3b+c=0

    But \textbf u is parallel to the xy-plane, so we must also have

    c=0\text.

    Substituting, that means 4a-3b=0\Rightarrow a=\frac34b\text. Choose an arbitrary pair of numbers that satisfy the equation to get a vector c\textbf u, and then find the unit vector in the same direction.
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    Thanks Reckoner your the best and I could understand it!
    I have another question hope you'll be able to answer it too!
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