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Simple vector arithmetic question 
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#1
Dec2813, 10:42 PM

P: 16

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 


#2
Dec2813, 10:46 PM

P: 4,037

Did you try to sketch some vectors and to come up with a counter example?



#3
Dec2813, 11:25 PM

P: 16

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. 


#4
Dec2813, 11:47 PM

P: 16

Simple vector arithmetic question
Nevermind I figured it out... I made a mistake by normalizing the resultant, which in turn messed up my final answer.



#5
Dec2913, 07:09 PM

Sci Advisor
P: 6,066

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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