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Math Help - Question on Vector Addition

  1. #1
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    Question on Vector Addition

    Greeting all,

    I have a question regarding the addition of two vector magnitudes. Generally I've read that we can use this formula:

    \sqrt{A^2 + B^2}

    But what is the different between that formula above and the one like this?

    \sqrt{A^2 + B^2 + 2ABcos\theta}

    I'm sorry if my question is too simple for this sub-forum section, I just seem to be confused with this very part.

    Thank You
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  2. #2
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    @Lites, you must be a lot more specific in the wording of your question.
    Really neither of those is correct without further qualifications.

    For example if you have a vector in \mathbb{R}^2 say \vec{U}=<a,b> then its length is \left\|\vec{U} \right\|=\sqrt{a^2+b^2}.
    That is close to your first example.

    Your second looks like your using the law of cosines.

    So, please try to clarify what you are asking.
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  3. #3
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    Quote Originally Posted by Lites View Post
    Greeting all,

    I have a question regarding the addition of two vector magnitudes. Generally I've read that we can use this formula:

    \sqrt{A^2 + B^2}
    First, what do you mean by "addition of two vector magnitudes". If you mean "find the magnitude of the sum of two vectors, having magnitudes A and B", then what you give is true only if the two vectors are perpendicular- it is from the Pythagorean theorem which applies to right triangles.

    But what is the different between that formula above and the one like this?

    \sqrt{A^2 + B^2 + 2ABcos\theta}
    This is the magnitude of the sum of two vectors having magnitudes A and B which form angle \theta, not necessarily perpendicular. Notice that if \theta= \pi/2, then cos(\theta)= 0 so you get the same thing as before. It is from the cosine law that generalizes the Pythagorean theorem to general triangles.

    I'm sorry if my question is too simple for this sub-forum section, I just seem to be confused with this very part.

    Thank You
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  4. #4
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    Quote Originally Posted by Plato View Post
    @Lites, you must be a lot more specific in the wording of your question.
    Really neither of those is correct without further qualifications.

    For example if you have a vector in \mathbb{R}^2 say \vec{U}=<a,b> then its length is \left\|\vec{U} \right\|=\sqrt{a^2+b^2}.
    That is close to your first example.

    Your second looks like your using the law of cosines.

    So, please try to clarify what you are asking.
    Sorry, what I'm trying to ask is when we should use those two formulas, in which case should we apply one of them.

    Quote Originally Posted by HallsofIvy View Post
    First, what do you mean by "addition of two vector magnitudes". If you mean "find the magnitude of the sum of two vectors, having magnitudes A and B", then what you give is true only if the two vectors are perpendicular- it is from the Pythagorean theorem which applies to right triangles.

    This is the magnitude of the sum of two vectors having magnitudes A and B which form angle \theta, not necessarily perpendicular. Notice that if \theta= \pi/2, then cos(\theta)= 0 so you get the same thing as before. It is from the cosine law that generalizes the Pythagorean theorem to general triangles.
    Ah yes now I understand! Thanks Ivy and Plato for the help!
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