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Thread: A couple of very simple questions about vectors and scalars

  1. #1
    Aug 2010

    A couple of very simple questions about vectors and scalars

    Dear MHF,

    I am a sophomore engineering student at The University of Tennessee (Go Vols!) and I am currently enrolled in Calc 3. I feel like I understand the more advanced concepts but struggle with the simpler stuff (like a person reading with no phonics, simply memorization). Therefore I feel like my basic knowledge needs to be boosted... hopefully the answers to these questions will help!

    1. Is a scalar the same thing as a vector's magnitude?

    2. Can a vector be made from a scalar?

    3. Additionally, how (in written notation) is it possible to tell the difference between the two? Like is one wrapped in abs value bars or what? Just a little confused about the context of all of this.

    Thank you, everyone!

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  2. #2
    Aug 2008
    1. It is true that a vector's magnitude is a scalar, but the definition of a scalar is not "the magnitude of a vector". The answer to this question can be as simple or as complex as your mathematical knowledge allows. Essentially, though, I think it's enough for most cases to say that scalars are known as such because they "scale" vectors in a vector space by either stretching them out or condensing them.

    2. I'm not sure I understand what you're asking, so correct me if I'm missing the mark. All you need to do to make a scalar into a vector is to multiply some vector by that scalar. For instance, if I define the vector $\displaystyle \vec {x}=(x_1, x_2, x_3)$ and then multiply it by the scalar 3, it becomes $\displaystyle \vec {x}^{'}=(4x_1, 4x_2, 4x_3)$.

    3. Vectors are denoted in a lot of different ways depending on where you come across them. As in the above example, many times vectors will have an arrow over them while scalars do not. You will often also see a vector denoted by a bold or italicized letter. Unit vectors can also sometimes be italicized letters, but in my experience have generally been denoted with a carat (^) above them. If you see a vector in absolute value bars, this is equivalent to the magnitude (or length) of the vector; otherwise, it is just the absolute value of a scalar.

    Consult your professor or TA if there is any doubt what some piece of notation means, since your grade is in their hands after all.
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