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Math Help - purpose of unit vector

  1. #1
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    purpose of unit vector

    hey everyone,

    so i've been doing vectors for quite some time now and eventhough i excel at vectors and calculus 3, what exactly is the point of having unit vectors. Why can't we just right them as normal vectors especially when i get to binormals and stuff, they always want unit vectors. Also, if you take the cross product of two unit vectors, do you end up with a unit vector. if not, can you please explain why not

    Thanks alot
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  2. #2
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    Re: purpose of unit vector

    Quote Originally Posted by ubhutto View Post
    what exactly is the point of having unit vectors. Why can't we just right them as normal vectors especially when i get to binormals and stuff, they always want unit vectors. Also, if you take the cross product of two unit vectors, do you end up with a unit vector. if not, can you please explain why not
    Unit vectors are used to standardize measurements.

    Let $u = \frac{1}{{\sqrt {14} }}\left\langle {1,2,3} \right\rangle~\&~ v = \frac{1}{{\sqrt 5 }}\left\langle { - 2,0, - 1} \right\rangle$

    What does $u\times v=?$.
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  3. #3
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    Re: purpose of unit vector

    unit vectors serve as a basis wrt which other vectors can be expressed. They are usually used as a unit orthogonal (orthonormal) basis ( a.a=1, a.b=0) , in which case the length of any vector is the sum of the squares of it's components.
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