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Simple vector arithmetic question

  1. Dec 28, 2013 #1
    I have two vectors: a = <ax, ay, az> and c = <cx, cy, cz>

    which have an angle of 45 degrees between them.

    If I get another vector by b = c - a then shouldn't b be orthogonal to a? I'm assuming this since a + b = c
    Last edited: Dec 28, 2013
  2. jcsd
  3. Dec 28, 2013 #2


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    Science Advisor

    Did you try to sketch some vectors and to come up with a counter example?
  4. Dec 28, 2013 #3
    Yes I have been using MATLAB to sketch and generate random examples. Here is one...

    a = <0.3814, 0.9023, 0.2010>
    c = <0.3965, 0.7378, -0.5463>

    The angle between these vectors is 45 degrees.

    I want a vector b such that b is orthogonal to a AND 45 degrees from c. Graphically speaking, this means a + b = c

    Solving for b,
    b = c - a = <0.0151, -0.1645, -0.7473>.

    But b dot a ≠ 0 therefore they aren't orthogonal. Why aren't a and b orthogonal?

    This happens for every random sample I make, starting with 2 vectors that are 45 degrees apart.
  5. Dec 28, 2013 #4
    Nevermind I figured it out... I made a mistake by normalizing the resultant, which in turn messed up my final answer.
  6. Dec 29, 2013 #5


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    Science Advisor

    The vectors you describe will form a triangle. With one angle at 45 deg. the other two angles could be anything that add up to 135 deg.
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