Simple vector arithmetic question


by The_Engineer
Tags: arithmetic, simple, vector
The_Engineer
The_Engineer is offline
#1
Dec28-13, 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
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A.T.
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#2
Dec28-13, 10:46 PM
P: 3,551
Did you try to sketch some vectors and to come up with a counter example?
The_Engineer
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#3
Dec28-13, 11:25 PM
P: 16
Quote Quote by A.T. View Post
Did you try to sketch some vectors and to come up with a counter example?
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.

The_Engineer
The_Engineer is offline
#4
Dec28-13, 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.
mathman
mathman is offline
#5
Dec29-13, 07:09 PM
Sci Advisor
P: 5,942
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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