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Squaring of vectors in absolute value

  1. Sep 26, 2013 #1
    Is |[itex]\vec{a}[/itex]+[itex]\vec{b}[/itex]|[itex]^{2}[/itex] equal to the same thing as ([itex]\vec{a}[/itex]+[itex]\vec{b}[/itex])[itex]^{2}[/itex]? And when is it equal to √(a[itex]^{2}[/itex]+b[itex]^{2}[/itex])?

  2. jcsd
  3. Sep 26, 2013 #2


    Staff: Mentor

    They're the same, assuming the implied multiplication in the expression on the right is the dot product. Otherwise, multiplication of one vector by another is not defined (with the exception of the cross product).
    Tip: You don't need so many tex or itex tags. Your squared vector sum can be written like this:
    [itex](\vec{a} +\vec{b})^2 [/itex]
    Or instead of the itex tags, you can use ## delimiters at the front and back.
  4. Sep 27, 2013 #3
    Thank you for the reply and the tip. But about the √(a^2+b^2)?? My second part of the question?
  5. Sep 27, 2013 #4
    That is merely the magnitude of both vectors. Assuming that's what you mean? You were a little unclear on the second part. Think of magnitude as the size or length of those two vectors.
  6. Sep 27, 2013 #5
    [itex]\sqrt{a^2+b^2}[/itex] is the magnitude of [itex]\vec{a}±\vec{b} [/itex],where [itex]\vec{a}[/itex] and [itex]\vec{b}[/itex] are orthogonal (perpendicular) vectors.
  7. Sep 27, 2013 #6
    Okay. Thank you, yes, it is exactly what I meant.
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