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Direction of cartesian equation

  1. Sep 10, 2015 #1
    1. The problem statement, all variables and given/known data
    In this question, I didn't see why the given 90 degree is 90 degree becoz it doesn't look like 90 degree. Can someone draw me a better diagram? It's hard to visualize it's 90 degree

    2. Relevant equations


    3. The attempt at a solution
     

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  2. jcsd
  3. Sep 10, 2015 #2
    Well it's trying to represent an angle measured in a 2D plane in 3D space on a 2D piece of paper. So it will always look skewed when the plane is not the same as the plane of the paper.
     
  4. Sep 10, 2015 #3

    RUber

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    They are trying to illustrate the 90 degree angles in 3D space. A common way to visualize this is to subractthe Z component, and you will clearly see the right angles in the x-y plane.

    The angles are 90 degrees by definition. You should not question it just because when it is illustrated at a skew angle it doesn't look like the square angle you are used to.

    The method being used is one that involves drawing a perpendicular line from the end of A to whichever axis you are interested in. Since your new coordinates are defined with angles to the vector A from a given axis, the definitions are given in terms of cosine(angle) = adjacent (axis) divided by magnitude (vector).
     
  5. Sep 11, 2015 #4
    well , i still dont understand . take an example , alpha already more than 90 degree. How can the other angle be 90 degree? Can you explain in other words , so that i can understand better ?
     
  6. Sep 11, 2015 #5

    SteamKing

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    How do you know alpha is more than 90° ? Remember, these are not plane triangles you are looking at. They are triangles in three dimensions which are drawn on a two-dimensional page.

    A better way to look at these diagrams is to imagine that the right angles are showing that there are three planes which are parallel to the x-y plane, the y-z plane and the x-z plane and which are also perpendicular to one another.
     
  7. Sep 11, 2015 #6
    I suggest you cut a corner off a piece of paper and view it at different angles to replicate the drawing views.
     
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