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Adding vectors?

  1. Jun 13, 2010 #1
    Alright, we have triangle abc with hypotenuse c. So, if you add vector a and vector b, the answer is vector c.

    Now, according to the pythagorean theorem, this would not make sense. But the pythagorean theorem is DISTANCE. I am guessing that this phenomenon has something to do with using displacement?
     
  2. jcsd
  3. Jun 13, 2010 #2

    Filip Larsen

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    Gold Member

    Note, that the pythagorean theorem corresponds to the particular geometric situation where vector a and b are orthogonal on each other and in this case, the pythogorean theorem relates the length of the three vectors. For general vectors a and b, you need the law of cosine that includes the angle between a and b in order to related the length of a and b with the length of c.
     
  4. Jun 13, 2010 #3
    My book says vector a + vector b = vector c. It uses (x,y) coordinates.

    Vector a: (x1,y1)
    Vector b: (x2,y2)
    Vector c: (x1+x2, y1+y2)

    Filip Larsen, what you just described gives me the magnitude of the displacement.

    Am I measuring distance or displacement? Is the vector all about displacement?
     
  5. Jun 13, 2010 #4

    jtbell

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    Staff: Mentor

    Displacement is only one example of a vector quantity. It's the first one that most physics textbooks introduce. There are many others: velocity, acceleration, force, momentum, angular momentum, electric field, magnetic field, ...

    In your example, the total distance traveled would be the sum of the lengths (magnitudes) of the displacement vectors a and b:

    [tex]d_{total} = \sqrt{x_1^2 + y_1^2} + \sqrt{x_2^2 + y_2^2}[/tex]

    The total displacement would be simply the vector c, which has magnitude

    [tex]\sqrt{(x_1 + x_2)^2 + (y_1 + y_2)^2}[/tex]

    and a direction (angle) given by

    [tex]\tan \theta = \frac{y_1 + y_2}{x_1 + x_2}[/tex]
     
  6. Jun 13, 2010 #5
  7. Jun 13, 2010 #6
  8. Jun 13, 2010 #7

    diazona

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    Homework Helper

    What do you mean by "Euclidean vectors"?
     
  9. Jun 13, 2010 #8
    Naty1's link is for Euclidean Vectors
     
  10. Jun 13, 2010 #9

    diazona

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    Homework Helper

    Oh, silly me :wink: should've clicked on that.

    From what I read in the article, it seems like a displacement vector is just one example of a Euclidean vector. Although it kind of depends on how you define "Euclidean vector" - there's a bit of ambiguity in the article, probably because different groups of people (e.g. physicists vs. mathematicians) have different definitions for the term.
     
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